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Mechanism of cation exchange process for epitaxy of superconducting mercury barium calcium copper oxide films and passive microwave devices

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Mechanism of Cation Exchange Process for Epitaxy of
Superconducting HgBa2CaCu2O6 Films and Passive Microwave
Devices
Hua Zhao
B.S., Harbin Institute of Technology, Harbin, China, 1983
M.S., Harbin Institute of Technology, Harbin, China, 1988
Submitted to the Department of Physics and Astronomy and the Faculty of the
Graduate School of the University of Kansas in partial fulfillment of the
requirement for the degree of Doctor of Philosophy
Dissertation Committee:
Chair: Dr. Judy Z. Wu
Dr. Hui Zhao
Dr. Siyuan Han
Dr. Douglas W. McKay
Dr. Brian B. Laird
Date Submitted:
UMI Number: 3295014
UMI Microform 3295014
Copyright 2008 by ProQuest Information and Learning Company.
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
ProQuest Information and Learning Company
300 North Zeeb Road
P.O. Box 1346
Ann Arbor, MI 48106-1346
The Dissertation Committee for Hua Zhao certifies
That this is the approved version of following dissertation:
Mechanism of Cation Exchange Process for Epitaxy of Superconducting
HgBa2CaCu2O6 Films and Passive Microwave Devices
Chair: Dr. Judy Z. Wu
Date approved:
ii
Abstract
The record high superconducting transition temperature (Tc) in Hg-based
High temperature superconducting (HTS) cuprates make them very promising for
both fundamental physics and practical applications. The high volatile nature of
Hg presents a major challenge in epitaxy of high quality Hg-based HTS films. In
a novel cation exchange process developed by our group recently, epitaxial
HgBa2CaCu2O6+δ (Hg-1212) films can be obtained by diffusing volatile Tl cations
out of, and simultaneously diffusing Hg cations into, the lattice of epitaxial
Tl2Ba2CaCu2O8 (Tl-2212) or TlBa2CaCu2O7 (Tl-1212) precursor films. Aiming at
the remained issues in understanding the mechanism of the cation exchange (CE)
process, this thesis work has studied the reversibility of CE. We have found that
the CE process is completely reversible between Hg-1212 and Tl-2212,
confirming further the thermal perturbation diffusion model. One of the
experimental works unveiled that the conversion from Hg-1212 to Tl-2212
involves two steps: conversion from Hg-1212 to Tl-1212 via CE followed by Tl
intercalation to form double Tl–O plans in each unit cell.
Two improvements have been made in raising the quality of the Hg-1212
films. First, by successfully introducing micro-channels in Tl-1212 precursor with
reversible CE, purer HTS Hg-1212 thin films have been obtained. Secondly, by
iii
pinning lattice with nonvolatile Re atoms, the surface morphology of Hg-1212
films have been improved.
In addition to making the high quality Hg-1212 films, we have fabricated
a two-pole X-band Hg-1212 microstrip filter and then investigated its nonlinearity
by measuring the third-order intermodulation (IM3) signals since the major
limitation for real application still comes from the nonlinearity. By a comparison
between different structural materials of Hg-1212, Tl-2212 and YBa2Cu3O7
(YBCO), the third-order intercept (IP3) of the Hg-1212 filter is consistently
higher than that in the YBCO and Tl-2212. The surprising similarity in the curves
of dc critical current density Jc and the rf JIP3 derived from the IP3 against
reduced temperature suggests that the magnetic vortex depinning in HTS
materials dominates the microwave nonlinearity at elevated temperatures. These
encouraging results have marked Hg-1212 out as a promising alternative material
for passive microwave devices at above 77 K operating temperature.
iv
This dissertation is dedicated to my husband
v
Acknowledgments
I have been fortunate in my career and my life to be surrounded by and to
work with great people. In this short page, I would like to thank my friends and
colleagues who helped me with the research works presented in this thesis.
First and foremost I must thank my advisor, Prof. Judy Z. Wu, for her
unfaltering support and excellent mentorship during my challenging graduate
school years, academically, metaphorically, and linguistically. I have the greatest
admiration for her command of condensed matter physics on both an
experimental and theoretical level and hope to one day have at least a comparable
amount of knowledge myself.
I would like to thank Prof. Siyuan Han for his great support in granting me
a full access of the microwave related facility in his laboratory, in addition to his
careful reviewing my research proposal in his extremely tight schedule.
I would also like to thank all other members of my thesis committee, Dr.
Brian Laird, Dr. Douglas McKay and Dr. Hui Zhao for reviewing my thesis.
Special thanks go to Prof. Douglas McKay, who has paved me a smooth path
towards establishing theoretical model regarding my research work, benefiting
from the courses taught by Him, Quantum Mechanics, Mathematical Physics, and
General Relativity.
vi
The experimental involving microwave characterization of high
temperature superconducting films could not be smoothly performed without the
help of Dr. Wei Qiu, who was working in Dr Han’s lab as PhD student that time.
Most heartfelt thanks go to Jonathan R. Dizon, Rose Lyn S. Emergo,
Rongtao Lu, and Xiang Wang, for many valuable discussions at the lab, countless
timely helps in their tight schedules, and enjoyable extracurricular activities at
homes.
Of course all of labmates and friends have been a great source of joy and
inspiration, throughout my time at KU. Thanks to everyone in the KU Thin Film
Group for being there during good and bad times, and for helping me out in my
research efforts in almost every way.
Last but not least, I would like to thank my parents Renliang Zhao and
Yuxian Guo for their love and continuous support during all the years I have spent
in another country, and my beloved husband Jingwen for his patience and
affection, which he demonstrated in so many most difficult periods of this thesis,
especially for his prayers before God. Finally, I would like to thank my dad, mom
and sister for their kind and loving support throughout the years I spent in
graduate school. My parents always enjoy boasting of my accomplishments, big
and small.
vii
List of Figures
Fig. 1.1 (a) A typical dependence of the resistivity on the temperature of a
superconductor [1.1]; (b) The reversibility of the diamagnetism in an ideal
superconductor [1.2]
Fig. 1.2 Comparison of flux penetration behavior of type-I and type-II.
superconductors with the same thermo-dynamic critical field Hc [1.1].
Fig. 1.3 (a) The mixed state, showing normal cores and encircling supercurrent
vortices; (b) Mechanism of flux-flow. The presence of current in a magnetic field
generates a Lorentz force, which tilts the staircase, allowing flux lines to hop out
of their pinning wells more easily [1.2].
Fig. 1.4 Typical layered structure of the cuprate HTS, two dimensional
superconductor. [1.4].
Fig. 1.5 Schematic diagram showing (a) Short coherence length and weak
interlayer coupling; (b) Pancake vortices due to weak SC interlayer coupling,
[1.5].
Fig. 1.6 Crystal structures of mercurocuprate HTS:HgBa2Can-1CunO2n+2+δ [1.6].
Fig. 2.1 Schematic description of the conventional thermal-reaction process in
which a material is formed via reaction of simple-compound precursor.
Fig. 2.2 Schematic description of the cation-exchange process in which the same
material is formed by replacement of a weakly bonded cation A in a precursor
matrix by a volatile cation B.
Fig. 2.3 Using different precursor structure Tl-2212 film, the lattice shrinks in caxis by ~13.3% (c=2.93nm to 1.27nm) [2.3].
Fig. 2.4 Dependence of superconducting properties on the operating temperature
[2.9].
Fig. 2.5. (a) Schematic of the diffusion mechanism in cation exchange, Path I:
layer-by-layer along c-axis Path II : By channeling through vertical defects and
then along a-b plane the rate along a-b plane is faster than that along c axis [2.6];
(b) The Hg-1212 volume portion converted from Tl-2212 precursor film in the
Hg–Tl cation exchange process is plotted as a function of the processing time.
The dashed and dotted lines are linear fitting of the period from t=0 to 1.5 h and
the period from t=1.5 to 12 h, respectively [2.7].
viii
Fig. 2.6 Large windows of processing temperature and vapor pressure have been
shown [2.3].
Fig. 2.7 Micrometer size of voids seen on the surfaces of thin films prepared with
cation exchange, lower operating temperature cannot solve this issue radically.
Fig. 3.1 Schematic diagrams of the lattice structure of (Tl, Re)-2212 film when
6% of Tl-2212 unit cells (textured symbols) are replaced with Re-1212 ones
(solid): (a) a plan view, and (b) a cross-sectional view.
Fig. 3.2 XRD θ−2θ spectra of (a) a Hg-1212 film fabricated using cation
exchange process; and (b) a (Hg, Re)-1212 film made under the same condition as
(a). The XRD θ−2θ spectra of their precursor films are also shown, respectively,
in (c) and (d). Both precursor films were about 0.25 mm thick. After cation
exchange, the film thickness reduced to 0.21 mm when the 2212 unit cells (c=1.48
nm) were transferred to 1212 cells (c=1.27 nm). All films were on (100) LaAlO3
substrates.
Fig. 3.3 SEM micrographs of (a) a superconducting Tl-2212 precursor film; and
(b) a (Tl, Re)-2212 precursor of film both annealed in thallium vapor at 820 °C
for 1 h in an Al2O3 crucible in flowing oxygen gas.
Fig. 3.4 SEM micrographs of (a) Hg-1212 film, and (b) (Hg,Re)-2212 film both
made using cation-exchange process in Hg vapor at 700 °C for 12 h.
Fig. 3.5 Magnetic susceptibility as a function of temperature measured in zerofield-cool mode on Hg-1212, (Hg, Re)-1212 films, and their precursor films. The
magnetic field was 10 Oe applied along the normal of the film.
Fig. 3.6 Temperature dependence of Jc of the Hg-1212 film (circle solid symbol)
and the (Hg, Re)-1212 film (square solid symbol) plotted (a) in the original Jc
scale and (b) normalized Jc scale [Jc /Jc(5 K)]. The inset of (b) replots the data in
(b) on the normalized temperature scale [T/Tc].
Fig. 3.7 (a) Jc−H curves at different temperatures of 5 K, 77 K, and 100 K for Hg1212 and (Hg,Re)-1212 films. (b) replots the same Jc’s at 77 K and 100 K on the
normalized Jc scale (Jc /Jc,0) . Jc,0 is the Jc at zero applied magnetic field.
Fig. 4.1 Schematic description of the Tl–Hg cation exchange occurring on the
“1212” structure. The crystal lattice remains nearly unchanged while the
superconducting transition temperature is altered between 85 and 90 K for Tl1212, and 120 and 125 K for Hg-1212.
ix
Fig. 4.2 Diffusion channel of “1212” structure (a) the diffusion of the Tl and Hg
cations may have to follow a layer-by-layer pattern. (b) the voids actually serve as
diffusion channels through the film thickness and therefore enable dominance of
ab-plane cation diffusion.
Fig. 4.3 XRD θ-2θ spectra of the sample films (a) a regular Tl-1212A film
annealed in an Al2O3 crucible in Tl vapor at 840ºC for 1 hour; (b) the Tl-1212B
film with micro-channels ; (c) the Hg-1212A film made from the Tl-1212A film;
(d) the Hg-1212B film from Tl-1212B film; All films except Tl-1212A made in
a sealed quartz tube in Hg vapor at 700º C for 12 hours to get target Hg-1212
films or in Tl vapor at 730º C for 2 hrs to achieve target Tl-1212B films.
Fig. 4.4 Scanning electron microscopy images of: (a) the regular Tl-1212A; (b)
The Tl-1212B film; (c) The Hg-1212A film made from Tl-1212A; (d) The Hg1212B film from Tl-1212B. (e) The Hg-1212AA film from Hg-1212A film
Fig. 4.5 Magnetic susceptibility as a function of temperature measured in zerofield-cool mode for the superconducting films. The applied field is 10 gauss and
perpendicular to the film.
Fig. 4.6 The Jcs of all Hg-1212 films at different temperatures (a) at 5K, (b) at
77K and (c) 100K and the inlets are the normalized Jc.
Fig. 4.7 Temperature dependence of resistivity (ρ) of Hg-1212A and Hg-1212B
films.
Fig. 4.8 XRD θ–2θ spectra of the sample films: (a) the starting Tl-2212 film; (b)
after its first cation exchange in Hg vapor at 700 °C for 12 h; (c) after a half-time
of the second cation exchange in Tl vapour at 760 °C for 1.0 h; (d) after
completion of the second cation exchange in Tl vapor at 760 °C for 2.0 h; (e) after
the third cation exchange in Hg vapor at 700 °C for 12 h; and (f) after the fourth
cation exchange in Tl vapor at 760 °C for 2 h. All films were made in sealed
quartz tubes except the starting Tl-2212 film.
Fig. 4.9 Schematic description of the two steps of the conversion from Hg-1212 to
Tl-2212.
Fig. 4.10 SEM images of a representative sample after several cation exchanges:
(a) after the first cation exchange in Hg vapor from a Tl-2212 precursor film; (b)
after the second cation exchange in Tl vapor; (c) after the third cation exchange in
Hg vapor; and (d) after the fourth cation exchange in Tl vapor.
Fig. 4.11 (a) Magnetic susceptibility as a function of temperature measured in
zero-field-cooling mode for a sample experiencing several cation exchanges. (b)
x
Comparison of the Jc values of the same sample in Hg-1212 phase after the first
and third cation exchange from Tl-2212. (c) Comparison of Jc values of the same
sample in Tl-2212 phase before any cation exchange (marked with Pre-Tl2212)
and after the second and fourth cation exchange from Hg-1212.
Fig. 5.1 Magnetic susceptibilities as a function of temperature of the Hg-1212 and
YBCO films measured in zero-field-cooled mode. The magnetic field was 10 Oe
applied along the normal of the film.
Fig. 5.2 Temperature dependence of critical current density (Jc) for all three types
of films.
Fig. 5.3 Comparison of plots of S21 vs. frequency for three types of filters: Hg1212, Tl-2212 and YBCO.
Fig. 5.4 (a) Schematic diagram of the experimental set-up for measuring IMD
signals. Inset: Design layout for the two-pole half-wavelength filter with width of
0.7 mm. (b) Input power versus the output power at different temperatures for the
Hg-1212 filter. Inset: the slop of the IM3 curves against reduced temperature.
Fig. 5.5 Plot of the IP3 values for Hg-1212, Tl-2212 and YBCO filters.
Fig. 5.6 Plot of the IP3 values for Hg-1212, Tl-2212 and YBCO filters at reduced
temperature scale. Inset: Temperature dependence of the dc critical current
density (Jc) for the three types of films before patterning.
Fig. 5.7 Normalized JIP3 /JIP3 (77 K) with Jc/Jc (77 K) against reduced temperature
for Hg-1212, Tl-2212 and YBCO patterned into the same type of microstrip
filters.
xi
Contents
Abstract ……...…………………………………………………………………...iii
Acknowledgments………………………………………………………………..vi
List of Figures..…………………………………………………...…………..…viii
Chapter 1
Introduction…………………………………………………........1
1.1 Brief Review of Superconductivity …………………………………………1
1.1.1 The Basic Phenomena………………………………………….…..1
1.1.2 The Theories of Superconductivity…………………………….…..5
1.1.3 Type I and Type II Superconductors and Flux Pinning……… ........9
1.2 Layered Structure of HTS……………………………………………………12
1.2.1 The Futures of Layered Structure in HTS…………………….......12
1.2.2 Hg-based HTS and its Special Feature…………………………...15
1.2.3 The Unique Properties of Hg-Based HTSs ……………………..18
1.3 Application of HTS at Microwave frequencies ……………………………..19
Chapter 2
Progresses in the Unique Cation Exchange Process…………......22
2.1. Difficulties in Preparation of Hg-based HTS………………………………..22
2.2 Novel Cation Exchange and its Advantages. …………………………..……24
2.2.1. Cation Exchange Processing............................................................24
2.2.2. Mechanism Study of Cation Exchange Process………………….28
2.3 Comparison between Cation Exchange and Conventional Methodology…...32
2.4. Some Solid Works Done in Our Group Using Cation Exchange ...………...33
2.5 Critical Issues Remained in Cation Exchange Processing…………………...36
2.6 Works Done in the Thesis ……………………………..………………….....39
Chapter 3
Pinning Lattice: Effect of Rhenium Doping on the Microstructural
Evolution to Hg-1212 Films……………………………………..41
3.1 The Working Principle of the Rhenium Doping……….………………….…41
3.2 Experiments and Results……………………………………………………..44
3.2.1. Crystalline Structure…………………………….…………………..45
3.2.2. Surface Morphology………………………………………….……..48
3.2.3. Superconducting Properties……..…………………………………..52
3.3 Conclusion…………………………………………………………………...56
Chapter 4 Reversibility of the Cation Exchange Process………………………..57
4.1 Generating Micro-Channels to Facilitate Tl-Hg Cation Exchange on
“1212” Lattice…………………………………………………………59
4.2 Converting Hg-1212 to Tl-2212 via Tl–Hg Cation Exchange in
Combination with Tl Cation Intercalation………………............72
Chapter 5
Nonlinearity of Two-Pole X-Band Hg-1212 Microstrip Filters…83
5.1 Nonlinearity in HTS Passive Microwave Devices…………………..…….84
xii
5.2 Fabrication and Characterization of Two-Pole Hg-1212 Filters…………….87
5.2.1 Transmission Properties between Hg-1212, YBCO and Tl-2212
Filters……….………...……………………...…………………………..87
5.2.2 Comparison of Third Order Intermodulation of Hg-1212 Filters with
YBCO and Tl-2212 Filters………………………………….……………91
5.3 Summary………………………………………………………………..…..100
Chapter 6
Conclusions and Outlook……………………………………….101
References………………………………………………………………………108
Publications……………………………………………………………………..116
xiii
Chapter 1
Introduction
1.1 Brief
Review
of
Superconductivity
and
High
Temperature
Superconductors
Superconductivity is one of the revolutionary discoveries within the past
century. Since its discovery, the research works have experienced several tides.
The latest tide is the highest one, which is still here and relates to high
temperature superconductors (HTSs), and has last over two decades. It is no
exaggeration to say that deeper impact on the science, technology and even our
daily life expects to come sometimes soon.
1.1.1 The Basic Phenomena
In 1911, the first observation of the superconductivity in mercury made
many people extremely excited because they observed, for the very first time,
resistless conductor at temperature T below a certain value Tc then [see Fig. 1.1
(a)] and believed that the old dream about the perpetual mobile had come true.
Many thought at that time the superconductor was a perfect conductor. In 1933,
after the verification of Meissner’s effect, scientists and engineers were full of
curiosity about this brand new thermodynamics state. Employing all theoretical
1
and experimental scientific means in electrodynamics, thermodynamics, quantum
mechanics plus wild imagination power, they could hardly have in-depth
understanding of this elusive new phenomenon for decades in many ways.
Illustrated in Fig.1.1 (b) is Meissner’s effect. When a magnetic field (not very
strong) is applied on superconductor at T>Tc, the magnetic flux penetrates
through the body of the superconductor.
However, if the superconductor is
cooled to T < Tc (so called superconducting state), the magnetic flux lines are
expelled out, namely, the magnetic field is zero inside the superconductor. In
another words, the superconductor works like a magnetic field screening entity,
working the similar way as a conductor screens an electric field.
Superconductivity, as a brand new physical phenomenon, has indeed
puzzled many scientists to establish a satisfied theoretical model. After over two
decades waiting of the discovery of Meissner’s effect, Nobel Prize winning BCS
(Bardeen, Cooper, and Schrieffer) theory has finally been published in 1957. The
key idea is: an (isotropic) attractive interaction leads to bind electron pair states
(“Cooper pairs”). A Cooper pair, as an entire entity that does not lose energy to
the lattice, can continue running through a ring superconductor for millions of
years after started, unless the temperature of the conductor is raised up over Tc[1.1]
Simply, it can be described as: in the superconducting state, the supercurrent is
carried by Cooper pairs, which are electron pairs bounded by a certain physical
interaction, such as a phonon-electron interaction, or a magnetic interaction.
2
(a)
(b)
Fig 1.1 (a) A typical dependence of the resistivity on the temperature of a
superconductor [1.1]; (b) The reversibility of the diamagnetism in an
ideal superconductor [1.2].
Cooper pairs’ binding energy can be expressed as 2∆ ≈ γ kBTc, where γ is
a fixed universal value according to BCS theory and varies between 1.9 to 7.0 for
different materials or different phases of the same material in HTSs [1.1].
3
Within decades after discovery of superconductivity, it had only been
observed below or around liquid helium temperature, too far away from room
temperature. Searching superconductors with higher temperature is of course a
great interest from the standpoint of applications.
In 1986, Bednorz and Müller discovered oxide high-temperature
superconductor (HTS), which can reach 35 K [1.3] in La-M (Ba, Sr, Ca)-Cu-O
ceramics at that time. After this turning point, through two-decade tremendous
efforts, scientists are still working on the models and techniques. In past 20 years,
cuprate HTS series have been greatly improved towards high materials quality
and can be in fact nowadays be prepared in a remarkably reproducible way.
However, the HTS materials quality level still need a lot more efforts to reach the
standards of classical superconductors for the reasons stemming from multipleelement attributes. Because of their liquid nitrogen operating temperature, the
pursuit towards real-world applications have driven intensive worldwide research
activities in last two decades, which can be seen by over 100 000 related
publications within this narrow field. From the perspective of applications, the
potentiality of real world research and development in microwave electronics and
transmission cables using YBCO has been envisioned right after the discovery of
HTSs. Currently, though cooling down from its overheat status of HTS field in
the last decade, many dedicated theoretical scientists as well as material scientists
are still cultivating in this field to seek breakthroughs both theoretically and
experimentally. In one hand, a theoretical model which can equate to the BCS
4
theory for the classical superconducting materials awaits to be established, in
another hand, the new techniques needed to be proposed to raise the samples
quality of the known HTSs, both bulks and films, also more desirable to raise
operating temperature further.
1.1.2
Theory of Superconductivity
After discovery of the superconductivity and then the verification of
Meissner’s effect, many theoretical models have been established, including the
phenomenological Landau-Ginzburg equations and the successful microscopic
BCS theory.
I. The Microscopic BCS Theory
The fundamental physical picture of the BCS theory is based on the
pairs of electrons (Cooper Pairs) as entities traveling through lattices without
energy dissipation. In the BCS theory, it was shown that an arbitrarily small
attraction between electrons in a metal can cause a paired state of electrons to
have a lower energy than the Fermi energy, which implies that the pair is
bounded. The attraction between electrons is indirect via electron-phonon
interaction, which applies well to low temperature superconductors (LTSs). The
indirect interaction proceeds when one electron interacts with the lattice and
deforms it; a second electron sees the deformed lattice and adjusts itself to take
5
advantage of the deformation to lower its energy. This leads to phononmediated electron-electron interaction that dominates the electron pairing.
Several important theoretical predictions have been derived directly from BCS
theory. These have been confirmed in numerous experiments as follows:
Since the electrons are bound into Cooper pairs, a finite amount of energy
is needed to break them apart into two independent electrons.
The ratio between the value of the energy gap (binding energy of Cooper
Pairs) at zero temperature and the Tc value (expressed in energy units)
takes the universal value of 3.528, independent of materials.
Eg(0)=2∆(0)=3.528 kTc,
The discontinuity of the electronic specific heat at Tc has been obtained.
The specific heat Ces(T) below Tc depends exponentially on the inverse
temperature:
Ces(T)= a exp.(-Δ/kBT).
This is in contrast to the normal state value Cen=γT. The normalized
magnitude of the discontinuity is
(Ces-Cen)Tc/Cen = 1.43
In its simplest form, BCS theory gives the superconducting transition
temperature in terms of the electron-phonon coupling potential and the
Debye cutoff energy:
6
k B Tc = 1.14hω c e
−1
N ( 0 )U 0
Where N (0) is the density of normal state electrons at the Fermi energy.
The hωc is related to the Debye cutoff energy. In addition, BCS theory
had predicted a theoretical limit of 30 K of Tc (due to thermal vibrations).
II. The Ginzburg- Landau theory
In 1950, Ginzburg and Landau introduced a complex pseudowavefunction ψ to describe the superconducting electrons. According to quantum
mechanics, the local density of superconducting electrons can be expressed as
ns= ψ
2
β
2
H
1
2
F = F n+α ψ + ψ +
(−ih∇ − 2eA)ψ +
2
2m
2µ0
2
4
where α and β are introduced phenomenological parameters, Fn is the free energy
in the normal phase, A the electromagnetic vector potential, and H the magnetic
field. Ginzburg-Landau equations were derived by simply minimizing the free
energy with respect to fluctuations in the order parameter and the vector potential.
2
αΨ + β Ψ Ψ +
J=
1
(−ih∇ − 2eA) 2ψ = 0
2m
2e ∗
[Ψ (−ih∇ − 2eA)ψ ]
m
7
where J is the electrical current density. The first equation determines the order
parameter ψ based on the applied magnetic field. The second equation provides
the superconducting current. The Ginzburg-Landau equations have brought many
interesting results. Perhaps the well known is the prediction of the existence of
two characteristic lengths in a superconductor. The first is called as coherence
length, denoted by ξ, given by
.
This characteristic length describes the size of thermodynamic fluctuations in the
superconducting phase. The second characteristic length is the London
penetration depth, denoted by λ and given by
where ψ0 is the equilibrium value of the order parameter in zero electromagnetic
field. The ratio κ = λ/ξ is called as the Ginzburg-Landau parameter, which is used
to differentiate Type I and Type II superconductors. Type I superconductors are
those with κ < 1/√2, and Type II superconductors are those with κ > 1/√2.
8
1.1.3
Type I and Type II Superconductors and Flux Pinning
Type I and Type II superconductors have dramatically different behaviors
in applied magnetic field H. Type I superconductor includes most metals, such as
titanium, aluminum, tin, mercury, and lead. The superconductivity in these
materials is destroyed when H exceeds the thermodynamic critical field Hc, below
which the Meissner state prevails. The value of Hc is related to the free-energy
difference between the normal and the superconducting state.
In type II superconductors, two critcal fields: lower critical field Hc1 and
upper critical field Hc2 exist. Below Hc1, the superconductor is in the Messiner
state and magnetic flux penetration starts when H exceeds Hc1 while
superconducting state remains. With increasing H, more magnetic flux penetrate
into the superconductor and the superconducting state is destroyed when H
reaches Hc2. While the class of type-I superconductors is composed entirely of
metallic chemical elements, type-II superconductors may be metal alloys or even
some pure metals, such as Niobium (Nb) and Vanadium (V), and also different
oxide compounds. All metals and metal alloys have their Tc below 30 K and are
referred to as low temperature superconductors (LTS), while the oxide
superconductors have their Tc above 30 K and are referred to as high temperature
superconductors (HTS).
9
Fig 1.2 Comparison of flux penetration behavior of type-I and type-II
superconductors with the same thermo-dynamic critical field Hc [1.1]
The flux penetration (B-H) curves in type-I and type-II superconductors
are depicted in the Fig. 1.2. A great advantage of type-II superconductors is that a
substantial critical current is present in the presence of H, which is critical to real
applications. Researches on flux pinning, flux creep, and flux flow in type II
superconductors in the so-called mixed state (Hc1<H<Hc2) have been the long
term topics for many groups. In the mixed state, the existence of normal regions
in the superconducting material is allowed [Fig. 1.3(a) and (b)]. When electric
current with density J is carried by a type-II superconductor, it passes the flux
lines and creates a Lorenz force FL = J × Φ0 upon each vortex. The quantized
magnetic flux or fluxons will remain in place as long as the pinning force F0 on
them is larger than the Lorenz force FL.
10
(a)
(b)
Fig 1.3 (a) The mixed state, showing normal cores and encircling
supercurrent vortices; (b) Mechanism of flux-flow. The presence of
current in a magnetic field generates a Lorentz force, which tilts the
staircase, allowing flux lines to hop out of their pinning wells more
easily [1.2].
11
At critical current density Jc, the Lorentz force will become greater than
the pinning strength, and fluxons will start to move [also see the drawing in Fig.
1.3 (b)]. This movement is referred to as flux-flow. Jc is an important parameter,
above which the material becomes resistive. In HTS, certain fluxon motion may
be activated by thermal fluctuation of the fluxons; this motion is slower and
random so it is called flux-creep.
1.2 Layered Structure of HTS
1.2.1
The Features of Layered Structure in HTS
HTSs are type II superconductors. This, together with their high Tc values,
make them promising candidates for superconducting devices including passive
microwave devices, power transmission cables and other electric devices and
systems. A main striking feature of cuprate superconductors is in their layered
structure, as shown in Fig. 1.4.
Almost all HTSs discovered so far can be
represented by a generic formula AmE2Rn-1CunO2n+m+n, where A, E, and R are
various cations, often with E = Ba, Sr, or Ca, and R = Ca or a rare-earth element
(see Fig. 1.4). They can be represented simply by Am2(n-1)n. For example, Hg1212, Tl-2212, and Hg-1223, we are going to use this notation frequently in the
rest of my thesis.
In order to show clearly the stacking sequence of this layered structure,
AmE2Rn-1CunO2n+m+n can also be written as (EO)(AO)m(EO)]{(CuO2) [R(CuO2)]n1},
illustrating the order of m (AO)-layers inserted between 2 (EO)-layers on top
12
of n (CuO2)-layers interleaved by (n-1) R-layers. As a result, n describes the
number of (CuO2)-layers per unit formula. The (AO)-layer may be replaced by a
complex oxide slab, or the R-layer by a complex (RO)-slab. Although they are
fairly complex at first glance, these layers can be grouped into two blocks: the
charge reservoir block (CRB) of (EO)(AO)m(EO)] and the active block (AC) of
{(CuO2)[R(CuO2)]n-1}. The CuO2 layers, which exist in all the HTS, are believed
to be the location of the mobile charge carriers in the cuprate family of HTS
compounds.
Fig 1.4 Typical layered structure of the cuprate HTS, two dimensional
superconductor [1.4].
HTS materials are extreme type-II superconductors with penetration
length λ > 100 nm and coherent length ξ up to 1 nm. This extreme short ξ
13
(comparable to the crystallographic length, a, b) make the HTSs special in many
ways. The superconductive coupling between these CuO2 layers [within a given
(CuO2/Ca/)n-1CuO2 stack ("interlayer coupling")] is much weaker than the
intralayer coupling within the CuO2 layers, but still much stronger than the
coupling between the (CuO2/Ca/)n-1CuO2 stacks which can be described as
Josephson coupling [Fig. 1.5(a)] [1.5].
This quasi-two-dimensional nature of superconductivity in HTS materials
leads to remarkable anisotropy of the superconducting properties. The Jc along
the CuO2 planes is much higher than that in the perpendicular direction, (a
property which is not at all appreciated with respect to technical applications but
can be compensated by additional engineering efforts). In some superconductors,
material imperfections with the dimension of the coherence length can serve as
“parking area” for vertex cores. As shown in the Fig. 1.5(b), without these
pinning centers, each layer has its own pancake vortex, much flexible and
independent. This is called quasi-disintegration of magnetic vortices. To bring
HTS materials into broader applications, there are many techniques have been
developed to increase the flux pinning effect and hence Jc. For example, one can
use high energy ion beams to generate columnar defects, which provide correlated
pinning when vortices are aligned with them and much enhanced Jc has been
obtained.
14
(a)
(b)
Fig 1.5 Schematic diagram showing (a) Short coherence length and weak
interlayer coupling; (b) Pancake vortices due to weak SC interlayer
coupling [1.5]
1.2.2 Hg-Based HTSs and Their Special Features
Fig. 1.6 depicts the structure of the Hg-based HTSs, which have the
highest Tc above 130 K among superconductors so far discovered.
The blocks (BaO)(HgOδ)(BaO) have the rock-salt structure, with a
thickness of about 5.5 Å. The alternating blocks (CuO2) [(Ca)(CuO2)](n-1) have a
perovskite-like structure, with an approximate thickness of [4.0 + 3.16(n-1)] Å.
The crystal structures for n = 1, 2, and 3 are schematically illustrated in the figure
above.
The crystal structures of Hg-based HTSs consist of two generic
building blocks: the vital, superconducting copper-oxide layers or planes, and the
insulating block layers, which can act as electronically active charge-reservoirs
for hole or electron donation to the copper-oxygen layers.
15
Fig 1.6 Crystal structures of mercurocuprate HTS:HgBa2Can-1CunO2n+2+δ
[1.6]
At the Hg atom site, many other kinds of atoms can fit in also to form
superconductors with suitable oxygen off stoichiometric ratio. Some researchers
(among them are Antipov’s research group) argued that Hg atoms are the best fit
because of the weak bond between Hg and O3. This weak bond actually, has less
impact on the bond between Hg and O2, thus the Cu-O1 plane near the perfect
plane, so the superconducting properties are the best [1.7]. This picture is in
agreement with the pressure dependence of the Tc number. Hg-atoms are the best
candidates for the highest Tc without external pressure. Actually, the angle for the
Cu-O1 plane is not most ideal one. When an external pressure is applied, this
angle can be adjusted towards the ideal value and higher Tc~166±1 K was
16
observed on fluorinated Hg-1223 at 23 GPa. At higher pressures, Tc begins to
decrease because the distortion pushes the Hg O1 plane over the best
configuration [1.7].
In fact, the real case is more complex in these multiple elements
(quaternary) compounds. However, this simple physical picture can provide us a
rough guidance when we want to optimize the properties by doping. We will
come back to this point later in my research work.
Interestingly, the Tc dependence on the periodic elemental table is shown
from the peer publications [1.8]. From the table there is an increase moving in the
periodic table from Pb to Hg. However, continuing to Au, the reported Tc is
already substantially lower. The trend is believed to be related to the chemical AO bond [1.8]. Actually, the ionic radii are complicated, the valence are also
playing active roles. However, we can conclude, the different elements occupy
the same site result in very different superconducting properties.
Another trend can also be seen from this table, that is: when the number of
CuO2 layer increases, namely, the number n increases in the general HTS formula,
the Tc increases monotonously at beginning, it peaked for a certain number.
However, many HTS scientists believe, the peak come from the limitation of the
difficulties of post oxygenation, as well as from the difficulties of the sample
preparation, because it is believed that the more CuO2 layers are formed from so
called “stack faults”. This means that after formation of Hg-1212, another stack of
CuO2 need to squeeze into the lattice, by intercalation.
17
Therefore, one can
imagine the difficulties in the preparation of the high quality materials, in the
forms of films or bulk.
1.2.3. The Unique Properties of Hg-Based HTSs
Among a few HTSs that have Tc above 100 K, Hg-based cuprate family
(usually formulated as HgBa2Ca(n−1)CunO(2n+2+δ), n =1, 2, 3), has attracted a great
attention since first reported concerning this family in 1991 [1.9-1.18]. Two
members, HgBa2CaCu2O(6+δ) (Hg-1212, n=2) and HgBa2Ca2Cu3O(8+δ) (Hg-1223
n=3) have stood out with excellent superconducting properties. Their remarkable
Tc values at ambient pressure, 124 K and 135 K, respectively, as well as critical
current density (Jc) up to 1MA/cm2 at 100K and self-field, have indeed made them
very attractive in high current-density applications and devices operating at above
100 K.
Considering high Tc and Jc values, growth of high quality epitaxial Hgbased HTS thin films is highly desirable for numerous applications. However,
high quality Hg-based HTS films are extremely difficult to be achieved due to
their intrinsic compositions of multiple elements plus their highly volatile nature
of Hg-based compounds. In addition, as a further complication, the large numbers
of adjacent phases in the phase diagram constituted by the contributing elements
hamper the preparation of phase pure samples, because the formation enthalpy of
the compound in one form differs only slightly from that in another. A
18
sophisticated process control during sample preparation is essential in order to
reduce the yield of samples.
1.3 Application of HTS at Microwave Frequencies
Over the last decade and a half, research on the microwave applications of
HTSs has been active and fruitful. The increasing interest was brought about by
the perceived potential on the marketability of superconducting electronics
especially in the wireless communications industry [1.19,1.20]. A large variety of
passive microwave devices have already been fabricated and characterized using
different HTSs including YBa2Cu3O7 (YBCO) and Tl2Ba2CaCu2O8 (Tl-2212)
[1.21-24]. The much improved performance of these HTS microwave devices
over their normal metal counterparts has been attributed to the nearly an order of
magnitude lower microwave surface resistance Rs of HTS films, which can only
be realized when the HTS devices are kept at liquid nitrogen temperature of 77 K
much below their Tc. Since a higher operation temperature implies lower capital
cost and system maintenance, HTS materials are advantageous for practical
applications such as microwave bandpass filters. Again, Hg-1212 is among few
HTSs with a Tc exceeding 120 K. Although comparable Rs [1.25] and power
handling capability [1.26] to that of YBCO and Tl-2212 at 77 K have been
observed on Hg-1212 films at much higher temperatures, little progress has been
made so far in application of Hg-1212 in microwave devices due to the
difficulties in epitaxy of large-area Hg-1212 films with sufficient uniformity. The
19
development of a cation exchange process [1.16] has resolved some major
technical issues in Hg-1212 film epitaxy and Hg-1212 films of dimension of
12×12 mm2 have been achieved recently [1.27]. Using this technique, we have
successfully fabricated two-pole X-band microstrip filters with Hg-1212 films and
characterized their microwave performance. The two-pole filter was selected
because of its simplicity in the design and ease in fabrication and packaging.
Studying the nonlinearity of microwave properties in HTS thin film
devices is of great importance for both applications and fundamental science.
From the viewpoint of applications, power handling capability of HTS films has
been substantially limited the applications HTS microwave devices since
nonlinearity deteriorates performance of the linear devices (filters, delay lines,
antennas) and hinders the optimization of properties of nonlinear devices
(modulators, switches, power limiters). At the standpoint of fundamental science,
delving into nonlinear properties allows the study of the dynamics of various
types of vortices in a unique way. It is believed that the power handling of HTS
films in the current state is most likely limited by extrinsic sources, such as
growth defects and impurities within the films. To identify the extrinsic origins of
nonlinearity, it is appropriate to correlate microwave, DC and morphological
characterizations
Microwave nonlinear properties of HTS films are usually studied by
measuring (i) the power dependence of the surface impedance, (ii) harmonic
20
generation and (iii) intermodulation distortion (IMD). Intermodulation distortion
has been chosen to investigate the nonlinearity in this research work.
My research work on microwave mostly concentrates on the nonlinear
properties in Hg-1212 films, with comparison with Tl2Ba2CaCu2Ox(Tl-2212) and
YBa2Cu3O7−δ (YBCO) films. Taking the advantage of the great progress made in
the fabrication of Hg-based HTS fims, some pioneer works have been performed
to fill the blank along this line.
21
Chapter 2
Development of Cation Exchange Process for Epitaxy of High
Quality Hg-1212 Films
2.1 Difficulties in Preparation of Hg-based HTSs
The conventional ex situ thermal-reaction process, which has been
extensively employed in preparation of Hg-HTS films, consists of two
consecutive steps (Fig. 2.1). In the first step, an amorphous Ba-Ca-Cu-O
precursor film is fabricated by any of several film deposition techniques such as
pulse laser deposition (PLD), magnetron sputtering, electron-beam, chemical
vapor deposition, etc [2.1]. Then the amorphous Ba-Ca-Cu-O precursor is reacted
in an evacuated quartz tube at high temperature around 800ºC, in controlled high
Hg-vapor pressure (5 to 10 atms) to form Hg-HTSs. The method of precursor
deposition (first step) is less important than the post-annealing (second step).
There are only three criteria that precursor films must meet to be used for
successful growth of good HTS films. First of all, it is important that the precursor
films be chemically stable in air to maintain both good adhesion to the substrates
and to remain chemically pure. Second, it is also helpful to have the elements
homogeneously mixed to limit the atomic diffusion necessary to form crystalline
structures. Finally, the precise cation composition of the precursor film on the
22
desired stoichiometry or off-stoichiometry is very important[2.1].
Having
prepared precursor films meeting three criteria mentioned above, now one can
move to next crucial step, the annealing process, in which is really the science of
growing HTS films. From the above brief overview about the HTS cuprates, it is
no surprise to see overwhelming difficulties in the fabrications of the Hg-HTS
samples with conventional thermal-reaction process.
Fig 2.1 Schematic description of the conventional thermal-reaction process in
which a material is formed via reaction of simple-compound precursor
The difficulties in epitaxial growth of Hg-HTS thin films are at least
threefold. Firstly, it is nearly impossible to accurately control the processing
parameters, such as Hg-vapor pressure, due to the highly volatile nature of the
Hg-based compounds. Actually, the Hg-based compounds have much lower
decomposition temperature, around 470ºC. When using these compounds as vapor
source, technically speaking, it is extremely hard to control a constant pressure.
From the brief analysis last paragraph base on the thermodynamic phase stability
research performed within last decade on the HTS’s, this results in typically
multiple superconducting impurities in Hg-HTS samples, which substantially
23
degrades the sample quality [2.1]. Secondly, Hg vapor reacts with most metals as
well as oxides, which prohibits epitaxial growth of Hg-HTS thin films on most
technologically compatible substrates. Even on a few chemically stable substrates
such as SrTiO3, serious film/substrate interface chemical diffusion was observed.
Consequently, most Hg-HTS films have to be made with large thickness (~1µm)
and most of them are c-axis oriented uniaxial films with rough surfaces. Finally,
the precursors are extremely sensitive to the air to form nonsuperconducting
phases such as Ca(OH)2 and CaCO3 phases which are hardly to decompose at
processing temperature ~800ºC. To overcome three main difficulties, some timeconsuming processes need to be applied, such as two-zone furnace processing and
glove-box processing. Tremendous efforts have indeed been recompensed by
some successes [2.2] although still far away from standards of the real world
applications.
2.2. Novel Cation Exchange Process and its Advantages
2.2.1. Cation Exchange Processing
In order to circumvent these difficulties in epitaxy of Hg-1212 films, our
group has developed a simple diffusive cation exchange technique (Wu,Yan and
Xie,1999) [2.3]. This process employs an epitaxial precursor matrix, instead of an
amorphous precursor film, and achieves epitaxial Hg-HTS films via replacement
of certain cations in the precursor matrix. The schematic diagram shown in Fig.
2.2 illustrates the cation exchange process. In the cation-exchange process, the
24
precursor matrices are chosen to have a similar structure and composition to that
of the target material. There is at least one weakly bonded cation (cation “A”) to
be replaced later by another cation (cation “B”) to form the target material. When
the cation A is perturbed using various methods such as thermal heating or
light/particle-beam irradiation, it will vibrate around the equilibrium site where
the Gibbs free energy is minimized. The spatial deflection of the cation A is
proportional to the energy of perturbation.
When the threshold perturbation
energy (Uth) is reached, at which the deflection of cation A is comparable to the
lattice constant, the cation A may escape from the site where it originally occupies,
leave the vacant site temporarily in the precursor matrix. In the cation exchange
process, however, the temperature, hence the perturbation energy is purposely
maintained to be close to a point so that the cation A is slowly escaping. If the
population of cation B in the mixed vapor of cation B+A is dominant, the vacant
site left behind by cation A will be occupied soon by cation B. One can see that
similar replacement can takes place for every single site after enough time given
to the processing and finally the target material is formed (refer to the cartoon in
Fig. 2.2 below).
25
Fig 2.2 Schematic description of the cation-exchange process in which
the same material is formed by replacement of a weakly bonded cation
A in a precursor matrix by a volatile cation B.
Using cation exchange process, the epitaxial Hg-1212 films have been
obtained successfully from both epitaxial Tl2Ba2CaCu2O8 (Tl-2212) and
TlBa2CaCu2O8 (Tl-1212) “precursor” films by replacing Tl cations on the lattice
with Hg ones [2.3-2.5] since (1) Tl-HTS’s are much less volatile, insensitive to
air, and easy to be obtained; (2) Tl-HTS’s have nearly the similar structures to
that of Hg-HTS’s . Fig.2.3 shows the conversion from Tl-1212 or Tl-2212 to Hg1212 films during cation exchange.
In this newly developed cation exchange processing, the sample
fabrication consisted of two steps: (1) preparation of epitaxial Tl-2212 precursor
films was followed by (2) conversion to epitaxial Hg-1212 films via Tl-Hg cation
exchange. In the first step, the precursor Tl-2212 thin films were deposited on
single crystal (100) LaAlO3 substrate at room temperature using dc magnetron
sputtering from a pair of Tl-2212 superconducting targets. A gas mixture of argon
and oxygen at a ratio of 4:1 was used for sputtering process. The as-deposited Tl-
26
2212 films were amorphous and nonsuperconducting. Superconductivity and
epitaxy were obtained after these films were annealed in a closed Al2O3 crucible
together with a pressed Tl-2212 pellet (Tl vapor source) and annealed at 820°C
for 1 h. It is worth pointing out here that unlike Hg vapor Tl is much less reactive
with substrates. In the second step, the Tl-2212 superconducting films obtained
from the previous step were sealed in an evacuated quartz tube together with two
pellets. One pellet was an unreacted Hg Ba2Ca2Cu3Ox pellet as Hg vapor source
and the other, a Ba2Ca2Cu3Ox pellet as Hg vapor absorber to balance the pressure
of the Hg vapor. The weight ratio between the former and the latter was 3:1. The
entire assembly was kept in a furnace at 700°C which is close to the threshold
perturbation energy (Uth=kBTth, 700°C) of Tl-2212 film for 12 h. The Hg-1212
films were then annealed in flowing oxygen at 300°C for 3 h to optimize their
oxygen composition. In this second step, the Hg vapor, which consist of high
speed flying molecules, cannot bombard the substrates directly, have much less
chances to diffuse into the substrates. In addition, because the crucial second step
in the cation exchange processing is most diffusive [2.6, 2.7], the requirement for
the controlling of Hg vapor pressure is much relaxed, the formation of poly phase
sample will be reduced dramatically. The extensive experiments done in our
group have supported this mechanism analysis here.
When Tl-2212 film is chosen as the precursor film, the two Tl-O layers
will collapse into one Hg-O layer to form Hg-1212 film during cation exchange.
27
The collapse will result in a disorder along a-b plane and the formation of the
voids, which we will mainly discuss later on.
2.2.2. Mechanism study of cation-exchange process
I. Threshold of the cation exchange
Because the cation–exchange process is a powerful way to prepare high
quality epitaxial Hg-HTSs films, the study of the mechanism is significantly
important to harness the processing to reproducibly generate thin films and
devices made of thin films. Some primary work done in our group paved a path
into this unexplored area. Firstly, it was confirmed that the cation exchange is
perturbation process that can performed in a large window of the processing
temperature. In fact, the Tl-Hg cation exchange was observed at the temperature
as low as 620ºC (sublimation temperature of HgO source is around 570ºC), which
is substantially lower than that required for the conventional process (typically ~
800ºC or higher for Hg-1212 phase). The rate of the cation exchange was proved
to increase monotonically with the operating temperature. For the same annealing
time, the completion of the cation exchange depended on the processing
temperature [2.9].
In the straightforward experiments, a possibility of cation exchange is
verified to qualitatively follow a relationship ~exp(-Uth/kBT), where Uth=kTth is
crystal lattice decomposing energy and kB is Boltzmann’s constant. To find out
Uth’s for Tl-1212, Tl-2212, and Hg-1212 films, Tl-2212, Tl-1212, and Hg-1212
28
films were heated at 0.8 atm O2 up to different temperatures and stayed for 1 h
and cooled down back to room temperature [see Fig. 2.4].
After each thermal cycle, the XRD θ-2θ spectra, Tcs and Jcs of the samples
were measured. At low temperature, the values were almost constant, however,
when the temperature reached over a certain temperature, the normalized Jcs
experienced a sharp drop (Tth,onset) and became zero at slightly higher
temperatures (Tth,zero). The sharp drop in Jcs was found to be accompanied by
dimishing of (001) peaks in the XRD spectra of the film, signaling collapse of the
crystal lattice. Taking the midpoint between the Tth,onset and Tth,zero as Tth, the Tths
for Tl-1212, Tl-2212, and Hg-1212 were 620ºC, 680ºC, and 780ºC (Fig.2.4). The
Tth defines the upper limit of the perturbation energy one might provide to a
precursor matrix without destroying it. The experiments thus performed has
confirmed this speculation, beyond this limit, the degraded quality of the films
indicated dramatic lattice collapsing [2.9].
One can see that Tth for Hg-1212 is slightly higher than that of Tl-1212
and Tl-2212. From the picture given above, it is expected that the cation exchange
from Hg-1212 to Tl-1212 is harder, thus need higher operating temperature. This
speculation was agreed with the experiments performed for verifying reversibility
in our group.
29
Fig 2.3 Using different precursor structure Tl-2212 film, the lattice
shrinks in c-axis by ~13.3% (c=2.93nm to 1.27nm). [2.3]
Fig 2.4 Dependence of superconducting properties on the operating
temperature [2.9]
30
II.
Diffusion mechanism in cation exchange
(a)
(b)
Fig. 2.5. (a) Schematic of the diffusion mechanism in cation exchange,
Path I: layer-by-layer along c-axis Path II : By channeling through
vertical defects and then along a-b plane the rate along a-b plane is faster
than that along c axis [2.6]; (b) The Hg-1212 volume portion converted
from Tl-2212 precursor film in the Hg–Tl cation exchange process is
plotted as a function of the processing time. The dashed and dotted lines
are linear fitting of the period from t=0 to 1.5 h and the period from t=1.5
to 12 h, respectively [2.7].
For the HTS materials, it is well known for their layered structures. In
these layered structure, it is reasonable to believe that there are two diffusion
direction, Path I: cation diffusion occurs layer by layer along the c-a axis, and
Path II: by channeling through vertical defects in the films such as voids and
growth defects, and then moving laterally along the a-b planes into grains [see Fig.
2.5(a) below][2.6]. Which diffusion process is dominant? The experimental
results suggest that the pathway of Hg cations in thin films (thickness < 0.5 µm) is
to channel through defects across the thickness of the films then diffuse into
grains along a-b planes and vice versa for Tl cations. A two stage model has been
proposed to explain the conversion from Tl-2212 to Hg-1212. At the first stage,
31
Tl-2212 collapse structurally into 1212 that contains both Hg and Tl when Hg
diffuses into grains, while at the second stage Tl cations diffuse out while Hg
cations diffuse in, resulting in the formation of pure Hg-1212 phase. A time
constant τ1 about 45-60 min was found for the first stage and the time constant τ2
beyond 2 τ1 for the second stage [refer to Fig. 2.5 (b)] [2.7].
2.3 Comparison between Cation Exchange and Conventional Methodology
In order to draw a clearer picture about the efficacy of the cation exchange,
let us choose the best values available and compare them with ones from cation
exchange processing. The table below lists some typical parameters which are
critical for real world applications. It is worthwhile to point out that for extremely
thin films, range from 50 nm to 80 nm, conventional methodology can hardly
fabricate any films, neither for films deposited on the metal substrates.
If merely judging from the plain numbers in the table above, one may put
a question mark on advantage of the cation exchange methodology. However, if
one knows that all the films from conventional processing come from timeconsuming dry-box operating with very low reproducibility, he (she) will happily
select highly reproducible cation exchange processing, which can be operated in
the air without anxiety about the degradation stemming from the carbon dioxide
and moisture.
32
Table I Comparison of critical superconducting properties of films
fabricated from conventional processing and cation exchange one.
Film/substrates
HgHg-1212/LaAlO3
HgHg-1223/LaAlO3
method
Conventional
Phase purity/
Thickness
Thickness
Jc(5K)/(77K)/(100K)
(MA/cm2), H=0
Pure/200Pure/200-300nm
116116-124K
20/3/1.5
Cation exchange Pure/200Pure/200-300nm
120120-125K
2020-40/240/2-5/0.55/0.5-2
Conventional
Predomin/200Predomin/200-300nm 120120-128K
Cation exchange Pure/300Pure/300-500nm
HgHg-1212/LaAlO3 Cation exchange Pure/50Pure/50-80nm
HgHg-1212/Ni
Tc(K)
Tc(K)
13/1.4/1.5
125125-130K
1010-20/120/1-1.5/0.11.5/0.1-0.5
110110-118K
55-10/0.710/0.7-1.1/0.11.1/0.1-0.4
Cation exchange Predomin/300Predomin/300-800nm 123123-125K
55-10/110/1-2/0.52/0.5-0.7
2.4. Some Solid Works Done in Our Group Using Cation Exchange
Surface morphology improvement
Although the collapse of the lattice has been evidenced in the conversion
between Tl-2212 and Hg-1212, the surface morphology of the resulted Hg-1212
films have shown surprisingly good quality, namely, they are much smoother than
its counterparts fabricated from the conventional processing, provided the
amorphous precursor films from the same sputtering processing were chosen for
better comparison. Judging from the fairly good surface morphology and X-ray
diffraction data, it seemed that the collapsing of the lattice is contained the scale
close atomic dimension or so. It is worth pointing out this better surface can only
be achieved when the operating temperature is lower than a certain threshold. The
remarkable surface improvement of the Hg-HTS film made in the cation
exchange process resulted in much better value of Jc, which has exceeded 1x106
A.cm-2 at T=100 K.
33
Low microwave surface resistance
It is no surprise that the better surface morphology can result in low
microwave surface resistance. In Hg-HTS films fabricated from cation exchange
methodology, the value similar to that of other HTS at 77 K, was observed at
temperature above 100 K. (10 GHz, ~0.2 mΩ at 77 K, and 0.3 m Ω at 120 K for
Hg-1212 film). This result suggests that Hg-1212 films are very promising for
microwave applications above 100 K [2.10, 2.11].
A large processing window
Cation exchange shows a different growth mechanism from conventional
thermal reaction process which requires stringent phase equilibrium.
a. Films processed at dramatically different Hg vapor pressure PHg of
1.0P0, 0.75P0, and 0.5P0 have nearly identical Tcs and Jcs.
b. The processing temperature range falls in range from 700ºC to 780ºC.
This flexible pressure and temperature requirements have indeed open a
door to modification of the Hg-HTS films to meet real world applications (see Fig.
2.6) [2.3].
Hg-HTS coated conductors
Hg-1212 films have been coated on biaxially textured Ni substrates
buffered with CeO2/YSZ/CeO2 trilayers with Tc=124 K, Jc=2.23×106 A/cm2
at 77 K and Jc= 0.73x106 A/cm2 at 100 K [2.12].
34
10
8
10
7
Precursor Tl-1212 film
0
10
5
10
4
10
3
c
a
0
a
b
c b
20 40 60 80 100 120
Hg-1212 film (1P 0)
T (K)
Precursor Tl-2212 film
o
Hg-1212 (700 C/12hr)
o
Hg-1212 (780 C/3hr)
Hg-1212 film (0.75P 0)
Hg-1212 film (0.5P 0)
2
6
-1
-1
10
7
10
6
10
5
10
4
J c (A/cm )
10
Magnetization (a.u.)
2
J c(A/cm )
Magnetization (a.u.)
0
0
50
100
T (K)
0
20
40
60
80
100
120
140
0
20
40
60
80
100
120
140
T (K)
T (K)
Fig. 2.6 Large windows of processing temperature and vapor pressure
have been shown.
Critical current density
Critical current density is doubled by fluorine-assisted oxygen
overdoping. It has been seen that the fluorine-assisted method help the
diffusion of the oxygen into the film as well as the uniformity.
The
crystallographic constant versus doping (annealing time) is also shown in
the experiments [2.13].
Sample dimension
Using cation exchange process, Hg-1212 films of 12x12mm2 with
uniform superconducting properties had been prepared [2.13].
Micro-strips fabrication
35
Micro-strips
made
of
Tl-1212
films
applying
standard
photolithography and converted to Hg-1212 devices in cation exchange
process successfully.
From the works just reviewed, we can see that the cation exchange
processing has indeed shed bright light to road towards further
improvement of the film fabrications. Using this cation-exchange technique,
one can circumvent the multifold road blocks confronted in the
conventional processing. Further efforts in microwave applications will
demonstrate the power of the cation exchange methodology.
2.5 Critical Issues Remained in Cation Exchange Processing
2.5.1 Voids on the Surface of Hg-HTS Films
Although the cation-exchange process provides a simple and highly
reproducible method for epitaxy of Hg-1212 films, these films are by no
means optimized, a number of large-size voids on the film surfaces still
worry us. From the SEM picture (Fig. 2.7) we can see a remarkable
difference from the films after conversion into the Hg-based films from Tl2212 films. The range of the voids dimension is from submicrometer to
several micrometers. As we reviewed in the last section, there are several
possible reasons for the formation of the voids. The first reason is that the
voids may be formed as the vertical channels for Tl-Hg exchange. Since no
similar voids were observed on Hg-1212 films converted from Tl-1212, the
36
voids formed in Hg-1212 film might be the exits through them the extra Tl
cations were evacuated out. The second cause might be the thermal
fluctuation, which shakes off a large number of Tl atoms from their
equilibrium sites in the lattice simultaneously, and hence results in collapse
of the lattice at macroscopic scale to form voids. The last possible reason is
the lattice collapse due to the conversion from double-layer Tl-O to singlelayer Hg-O, resulting in a disorder (dislocation) along a-b plane and causing
the formation of the voids.
These voids can be scattering centers to electromagnetic waves that
are propagating along the superconducting films and cause significant loss.
This might explain the lower microwave power handling capability of Hg1212 films in the normalized temperature scale as compared to its yttrium
barium copper oxide and Tl-2212 counterparts. Moreover, these voids
provide entrance channels for moisture and other contaminants, making
Hg-1212 films vulnerable even in standard characterization and device
fabrication processes. This problem may be partially solved by lowering
cation exchange processing temperature so as to reduce the probability that
many Tl cations are thermally excited out of the lattice simultaneously from
the same local area. Indeed, the void population was reduced (15) when the
processing temperature was decreased from ~800 °C to ~700 °C but the
dimension of the voids remained more or less the same. This is not
surprising since simply lowering the processing temperature does not imply
37
a fine control over the Tl diffusion pattern at a microscopic scale. In
addition, the cation exchange becomes much less efficient at temperatures
close to the binding energy of Tl cations, 700 °C to the Tl-2212 lattice. So,
we need to find a new avenue to reduce the size of voids.
r
3h
º C/
780
Precursor—Tl2212 film
700ºC
/12hr
Fig 2.7. Micrometer size of voids seen on the surfaces of thin films
prepared with cation exchange, lower operating temperature cannot solve
this issue radically.
2.5.2 The Reversibility and Applicability of Cation Exchange Methodology
After a brief review about the cation exchange processing, its procedure,
its mechanism, and its efficacy of making Hg-HTS films, as well as the
comparison between the conventional processing and cation exchange one, it is
natural to seek the expanding applications of the newly developed powerful
means to harness processing of other materials that have one volatile element. If
the same scheme of the cation exchange is also applicable to other volatile
materials that are difficult to obtain in conventional process? What are the
necessary and sufficient conditions for the cation exchange to occur?
38
2.5.3 Nonlinearity in Microwave Devices
In our previous study, we have observed low microwave surface resistance
(Rs) and high power handling capability in Hg-1212 films and microstrip line up
to 110 K. Developing the Hg-1212 microwave devices and investigating
mechanism of nonlinearity in microwave devices, which limits the real
application, are the important issues so far.
2.6 Works done in my thesis
In chapter 3, we introduce a new method to eliminate such large-scale
voids stemming from lattice collapse. “Lattice pins” were introduced on the
original Tl-2212 lattice by partially replacing volatile Tl cations with nonvolatile
Re ones. Since the Re cations remain on the lattice during the Tl-Hg cation
exchange, they pin the lattice around them. HgBa2CaCu2O6 films obtained from
these Re-doped Tl-2212 precursor films have much improved microstructures
with the pore dimension reduced by an order of magnitude.
A detailed works regarding reversibility of the cation exchange processing
have been fully described in Chapter 4. Firstly, we have demonstrated the
conversion from Hg-1212 to Tl-2212 structure can be achieved at relatively
higher Tl vapor pressure and the conversion consists of two steps: from Hg-1212
to Tl-1212 via Tl–Hg cation exchange on the ‘1212’ lattice followed by Tl-1212
to Tl-2212 via Tl cation intercalation. Secondly, by introducing micro-channels
39
and consequently completion of cation exchange processing as well as
superconducting characteristics with more runs of processing carried out. The
obvious increase of critical current density Jc in the Hg-1212 film out of third
cation exchange conversion demonstrated the major role played by two-pathways
diffusion processes, i.e. the dominant cations diffuse into the films through the
channel pathways originated from vertical defects across the thickness of films
and then followed by diffusion within a-b planes.
Since nonlinear effects in HTS passive microwave devices are considered
to be the major cause that limits the power handling capability of the devices, in
Chapter 5, third-order intermodulation is studied in two-pole X-band hightemperature superconducting Hg-1212 microstrip filters at > 77 K. The thirdorder intercept (IP3) of the Hg-1212 filters is consistently higher than that of the
YBa2Cu3O7 filter of the same geometry in this temperature range. At 110 K, the
IP3 of 38 dBm remains for the Hg-1212 filters, the best so far achieved at T > 100
K. The dc critical current density Jc and the rf one JIP3 derived from the IP3 have a
similar reduced temperature dependence, suggesting that the magnetic vortex
depinning in HTS materials dominates the microwave nonlinearity at elevated
temperatures.
40
Chapter 3
Pinning Lattice: Effect of Rhenium Doping on the
Microstructural Evolution to Hg-1212 Films Pinning Lattice
3.1 The Working Principle of the Rhenium Doping
In the previous chapter, we have discussed the voids formed on the surface
of Hg-HTS films, which are undesirable for applications. Then a question arises
naturally: how to limit the sizes of the voids if not possible to completely prevent
the formation of the voids during the cation exchange processing?
Chemical doping/substitution may provide a direct solution to the voidforming problem by modifying diffusion patterns of Tl cations out of the lattice at
a microscopic scale. In the cation exchange process, the thermal energy provided
to the crystal lattice causes deflection of atoms. The weakly bonded volatile
elements, such as Tl, may acquire enough energy to break their bonds from the
lattice while other elements remain. This lattice deformation may occur at a
macroscopic scale if a large number of volatile elements leave the lattice
simultaneously. If the volatile elements, such as Tl in Tl-2212, are replaced
partially with nonvolatile elements, the nonvolatile cations remain on the lattice
during the cation exchange so as to pin the lattice and to minimize macroscopic
lattice deformation. Many elements, such as Re [3.1-3.3], Bi [3.4] and Pb [3.5]
41
may be chosen to replace Hg in the Hg-1212 lattice. Among others, Re is of
special interest because of its benefits to Hg-1212. There are at least three reasons
that Re atoms can help to raise the quality of the outcome films.
1. Re cations have been probed to be of high valence (6.01-6.84+) in the sites
where the Tl or Hg-cations originally occupied, so these introduced Re
cations can prevent excess formation of the oxygen vacancies, which are
believed to be responsible to the metastablity of Hg-based cuprate samples.
2. The radius of the Re cation is much smaller than that of Hg and Tl cations,
consequently, Re-O bond lengths are detected much shorter than the
corresponding Hg-O distances. The lattice distortion originates from these
ions contraction might lead columnar defects at least for a few layers of
the CuO blocks and then could serve as flux pinning centers because of
relatively short coherence length in the layer-structural cuprate HTS
superconductors.
3. Addressing the void formation issue we brought at the beginning of this
paragraph, in our cation exchange approach, this nonvolatile Re element
can serve as lattice pins that can form a collapse-proof matrix. When mass
Tl cations escape from their sites simultaneously due to higher processing
temperature, the matrix can serve as framework preventing collapse in
large scale.
It is also worthwhile to mention here our selection is inspired by the
reported results that have shown the Re-doping can prevent contaminating of CO2
42
and moisture. Indeed, the material stability of Hg-based films has been
remarkably improved through doping Re to the Hg sites, and the sensitivity of
precursors and superconducting phases against CO2 has also been reduced. In
addition, the irreversibility field was improved in Re-doped Hg-1223, this actually
agreed with the shortening of the blocking layer, despite a slightly lower Tc.
In this cation exchange process, the nonvolatile dopants need to be
inserted in the precursor lattice. This is illustrated schematically in Fig. 3.1 with
Re taken some of the Tl sites in the Tl-2212 unit cells. During the Tl-Hg cation
exchange, the Re cations will remain on the lattice to pin the lattice and to
minimize macroscopic lattice deformation. In another words, the “pinning lattice”
formed with Re can prevent macroscopic collapse even when the Tl atoms escape
rapidly. A plan view of the model is shown on the left side [Fig. 3.1(a)], the solid
dots represent Re ions. A cross-section view is shown on the right side [Fig.
3.1(b)]. You might notice that we have marked that Tl-2212 and Re-1212 with
different phases. We’ll discuss this in more details later on at experimental parts.
In this work, we have successfully synthesized the doped (Tl1.88Re0.12)-2212
[(Tl,Re)-2212 in the rest of the text] films on LaAlO3 substrate and converted
them to (Hg0.94Re0.06) -1212[(Hg,Re)-1212 in the rest of the text] using the cationexchange process. Indeed, a dramatic improvement in the film microstructure was
observed on Re-doped Hg-1212 films.
43
Re
Tl
Tl
Re
Tl
Tl
Tl
Tl
Tl
Tl
Tl
Tl
Re
Tl
Tl
Re
(a)
Tl-2212
Re-1212
(b)
Fig 3.1 Schematic diagrams of the lattice structure of (Tl, Re)-2212 film
when 6% of Tl-2212 unit cells (textured symbols) are replaced with Re1212 ones (solid): (a) a plan view, and (b) a cross-sectional view
3.2 Experiments and Results
Sample fabrication consisted of two steps: preparation of epitaxial (Tl,Re)2212 precursor films was followed by conversion to epitaxial (Hg,Re)-1212 films
via Tl-Hg cation exchange. In the first step, the precursor (Tl,Re)-2212 thin films
were deposited on single crystal (100) LaAlO3 substrate at room temperature
44
using dc magnetron sputtering from a pair of (Tl1.88Re0.12)-2212 superconducting
targets. The rest of condition is the same as that described in previous chapter.
3.2.1 Crystalline Structure
The crystalline structure and phase purity of the films were analyzed using
x-ray diffraction (XRD). Fig. 3.2 depicts the XRD θ-2 θ spectra of (a) Hg-1212,
and (b) (Hg, Re)-1212 films and their precursor (c) Tl-2212, and (d) (Tl,Re)-2212
films, respectively. All films are c-axis oriented and the amount of impurity
phases is negligible. The (Hg, Re)-1212 film has a nearly identical structure to the
undoped Hg-1212 as shown in Figs. 3.2(a) and 3.2(b). Interestingly, their
precursor films had a subtle difference in structure. Without doping, only “2212”
lattice structure is visible [see Fig. 3.2(c)]. In the case of Re doping [see Fig.
3.2(d)], some additional peaks marked with * are clearly visible. A comparison of
Fig. 3.2(d) with Figs. 3.2(a) or 3.2(b) suggests that these peaks are from “1212”
phase. This means that certain amount of 1212 phase was formed in the Re-doped
Tl-2212 precursor films. Theoretically speaking, both Tl-1212 and Re-1212
structures are possible. We, however, argue that the latter may occur at a much
higher probability based on the following reasons. First, the processing condition
used was favorable to Tl-2212, which has been confirmed by the fact that no Tl1212 was formed in the undoped case [see Fig. 3.2(c)]. On the other hand, Re2212, similar to Hg-2212, is much less stable than Re-1212 (Hg-1212) and special
processing condition, such as high vapor pressure plus chemical replacement on
45
the Hg or/and Ca sites, is required to form “double-layer” structure.[3.6, 3.7]
Based on these considerations, we propose that the Re-doped Tl-2212 is
composed of pure Tl-2212 and Re-1212 phases. If no phase segregation occurs,
Re-1212 unit cells should be present uniformly in the lattice of Tl-2212. Since the
c-axis lattice constant of Re-1212 is 1.27 nm while that of Tl-2212 is 1.48 nm, the
mixing of the Re-1212 phase in Tl-2212 lattice will result in antiphase grain
boundaries, as schematically illustrated in Fig. 3.1(b), in the first several to
several tens of monolayers. These antiphase grain boundaries have been observed
on YBa2Cu3O7 films grown on miscut substrates and they later develop into
dislocation type of growth defects at larger film thickness [3.8, 3.9].
46
Fig 3.2. XRD θ−2θ spectra of (a) A Hg-1212 film fabricated using cation
exchange process; and (b) a (Hg, Re)-1212 film made under the same
condition as (a). The XRD θ−2 θ spectra of their precursor films are also
shown, respectively, in (c) and (d). Both precursor films were about 0.25
mm thick. After cation exchange, the film thickness reduced to 0.21 mm
when the 2212 unit cells (c=1.48 nm) were transferred to 1212 cells
(c=1.27 nm). All films were on (100) LaAlO3 substrates.
47
3.2.2 Surface Morphology
The scanning electron microscopy (SEM) micrographs of the Tl-2212 and
(Tl,Re)-2212 precursor films are shown in Figs. 3.3(a) and 3.3(b), respectively.
The surface morphology of the latter [Fig. 3.3(b)] is nearly featureless, much
smoother than that of the undoped Tl-2212 film [Fig. 3.3(a)]. In addition, the
impurity phases (mostly the intermediate oxide compounds) typically observable
on undoped Tl-2212 films due to contamination of the simple oxides precursor
materials in air [see Fig. 3.3(a)] disappeared in the case of Re doping. This
suggests Re doping reduces air contamination of the Tl-2212, which is similar to
what has been observed for Hg-1212 and Hg-1223 cases. On Fig. 3.3(b), many
small size “holes” of tens of nanometers in diameter can be clearly seen.
By carefully examining the surface of undoped Tl-2212 [Fig. 3.3(a)], we
conclude that this is unlikely related to Re doping since the holes are present also
on the undoped Tl-2212 films. Nevertheless, those holes are not as obvious on the
undoped Tl-2212 films simply because they are covered by many surface
impurity particles. The mechanism of the hole formation remains unclear at this
point. One possibility is that they may be the pathways for Tl diffusion during the
Tl vapor processing. Further experiments are necessary to pinpoint this
mechanism.
48
Fig 3.3. SEM micrographs of (a) a superconducting Tl-2212 precursor
film; and (b) a (Tl,Re)-2212 precursor of film both annealed in thallium
vapor at 820 °C for 1 h in an Al2O3 crucible in flowing oxygen gas.
Figures 3.4(a) and 3.4(b) depict the SEM micrographs of Hg-1212 and
(Hg, Re)-1212 films obtained via cation exchange process from Tl-2212 and (Tl,
Re)-2212 precursor films, respectively. A remarkable difference between these
two films is the reduced void dimension with Re doping, suggesting that the
crystalline lattice deformation pattern was indeed modified by doping Re on Tl2212 lattice. In the undoped case, the dimension of the voids is in the range of
submicrometer to several micrometers [see Fig. 3.4(a)] while with Re doping, the
average dimension of the voids is in the range of tens of to 3 hundreds
49
nanometers, and the average size of the voids is about 150 nm. It reduced by an
order of magnitude [see Fig. 3.4(b)]. The void density of the (Tl, Re)-2212
precursor film is 0.6 on a 10 µm2 area, while that of the (Hg, Re)-1212 is 4.6 on a
10 µm2 area. However, it is hard to tell if the voids on the precursor are inherited
to the (Hg, Re)-1212 film. It should be realized that this reduced void dimension
is two orders of magnitude larger than what is expected theoretically. When 6% of
unit cells of Tl-2212 are replaced with Re-1212 ones, the void dimension should
be less than 1.6 nm (both Re-1212 and Tl-2212 have their an axes around 0.4 nm)
if the two types of unit cells formed an alloy. The observation of the much larger
dimension of the voids suggests that phase segregation may occur in (Tl, Re)2212. This argument is supported by the observed Re-1212 phase in XRD data
[Fig. 3.2(b)]. This phase segregation is in fact not unexpected because of large
lattice mismatch between Tl-2212 and Re-1212 along the c axis. The strain
generated by this lattice mismatch may serve as the driving force for the phase
segregation.
Another fact consistent with this argument is the difficulty we have
encountered in doping higher percentage Re in Tl-2212 lattice. Dramatically
roughened surface morphology was observed when the Re-doping level was
doubled. The size of Re-1212 colonies after the phase segregation can be
estimated by assuming that the collapsed Tl-2212 colonies are a hundred times
bigger in dimension than the theoretically expected value of 1.6 nm. A
simpleminded calculation suggests 104 unit cells of Re-1212 in each Re-1212
50
colony with dimension of 40 nm along each side if the colony is a square.
Transmission electron microscopy with adequate spatial resolution would be ideal
to confirm this and will be certainly a topic of future research (unfortunately, such
a facility is not available locally at this point).
Fig 3.4 SEM micrographs of (a) Hg-1212 film, and (b) (Hg, Re)-2212
film both made using cation-exchange process in Hg vapor at 700 °C for
12 h.
51
3.2.3. Superconducting Properties
Figure 3.5 depicts the temperature dependence of the magnetic
susceptibility of Hg-1212 (solid squares) and (Hg, Re)-1212 (solid triangles) films
measured in a 10 Oe magnetic field (H) applied along the normal of the film. Both
films showed superconducting transition above 110 K. The Tc of (Hg, Re)-1212
films was typically in the range of 114−118 K, slightly lower than that of the
undoped Hg-1212 film (120−124 K). Interestingly, lower Tc’s were also reported
previously on most chemically doped Hg-1212, including Re-doped ones.
Fig 3.5 Magnetic susceptibility as a function of temperature measured in
zero-field-cool mode on Hg-1212, (Hg, Re)-1212 films, and their
precursor films. The magnetic field was 10 Oe applied along the normal
of the film.
The susceptibility vs. temperature curves for the Tl-2212 (open squares)
and (Tl, Re)-2212 (open triangles) measured under the same experimental
conditions were also included in Fig. 3.5. It has been noticed that Tc’s of the Tl2212 films were also slightly higher than that of (Tl, Re)-2212 films. Since post
oxygen anneal did not improve the Tc’s of Re-doped Tl-2212 and Hg-1212 films,
52
we speculate that Re dopants may disturb the local oxygen distribution in both the
2212 and 1212 lattice, which in turn lowers the Tc of the material.
Fig 3.6 Temperature dependence of Jc of the Hg-1212 film (circle solid
symbol) and the (Hg, Re)-1212 film (square solid symbol) plotted (a) in the
original Jc scale and (b) normalized Jc scale [Jc /Jc(5 K)]. The inset of (b)
replots the data in (b) on the normalized temperature scale [T/Tc].
53
Jc’s were calculated using the Bean model from the magnetization vs.
magnetic field hysteresis loops measured at different temperatures. The magnetic
field was applied along the normal of the film. Figure 3.6 shows a typical
comparison of the self-field Jc as function of temperature for a pair of
representative Hg-1212 and (Hg, Re)-1212 films. The Jc in the former is typically
higher by a factor of 1.5–3 than that of the latter in the whole temperature range
from 5 K to 100 K. For example, the Jc’s of the undoped Hg-1212 are 15.6, 3.2,
and 1.0 MA/cm2 at 5 K, 77 K, and 100 K respectively, while those for the
(Hg,Re)-1212 are 8.0, 1.2, and 0.38 MA/cm2 at the same temperatures [see Fig.
3.6(a)]. This represents the typical behavior among all the films we have studied.
The Jc ratio between the Hg-1212 and (Hg, Re)-1212 films increases slightly with
increasing temperature, as shown in Fig. 3.6(b). This slightly higher Jc ratio at
higher temperature may be attributed to the lower Tc of the (Hg, Re)-1212. Indeed,
the two Jc curves almost coincide when Fig. 3.6(b) is replotted on the normalized
temperature scale (T/Tc) as shown in the inset of the Fig. 3.6(b). It is, however,
unclear why the overall Jc is lower in the Re-doped Hg-1212 films.
Figure 3.7 compares the magnetic field dependence of Jc in the two types
of films at 5 K, 77 K, and 100 K. Subtle difference is visible. Despite an overall
higher values as shown in Fig. 3.7(a), the Jc in the undoped Hg-1212 film
decreases faster with increasing field in the low field range. This can be better
demonstrated when the same curves are plotted on the normalized scale (Jc /Jc,0) in
Fig. 3.7(b). This indicates the magnetic flux pinning is enhanced with Re doping,
54
consistent with what was previously reported by other groups. At higher field, the
two Jc -H curves cross over and both drop sharply when the field is further
increased.
Fig 3.7 (a) Jc−H curves at different temperatures of 5 K, 77 K, and 100
K for Hg-1212 and (Hg, Re)-1212 films. (b) replots the same Jc’s at 77 K
and 100 K on the normalized Jc scale (Jc /Jc,0) . Jc,0 is the Jc at zero
applied magnetic field.
55
3.3 Conclusion of This Chapter
In
conclusion,
we
have
fabricated
epitaxial
c-axis
oriented
(Hg0.94Re0.06)Ba2CaCu2O6 films by replacing the Tl cations from an epitaxial
(Tl1.88Re0.12)Ba2CaCu2Ox precursor films in the cation-exchange process. It was
found that the presence of nonvolatile Re on the precursor lattice pins the lattice
locally so as to reduce the large-scale lattice collapse, which occurs on undoped
Tl-2212 precursor lattice and typically results in micrometer size voids in Hg1212 films after the cation exchange processing. By pinning the lattice with Re
doping, the void size has been reduced by an order of magnitude and the surface
morphology has been improved dramatically. In addition, this result has also
demonstrated for the first time that Tl-2212 precursor lattice doped with
nonvolatile elements on the volatile Tl sites can be employed for epitaxy of
chemically doped Hg-1212 films in cation exchange process, enabling tailoring
microstructure and physical properties of Hg-1212 films in a much controllable
fashion.
56
Chapter 4
Reversibility of the Cation Exchange Process
As already reviewed earlier, using the cation exchange methodology,
epitaxial thin films of HgBa2CaCu2O6 (Hg-1212) exhibiting superior physical
properties have been obtained from epitaxial precursor films of Tl-1212 (y = 1
and z = 1) or Tl-2212 (y = 2 and z = 1)[4.1–4.6]. Despite the exciting results
obtained, the mechanism of the cation exchange has been the subject of debate
ever since it was developed. Understanding this mechanism is important not only
because cation exchange has provided a vital scheme for the epitaxy of Hg-HTS
films, but also because it may be developed into a generic “atomic surgery”
scheme for the synthesis and epitaxy of other volatile materials. So, a genetic
question rises: is cation exchange process reversible? If the answer is a yes, what
is the underlying mechanism? Motivated by this, we have recently carried out a
study on the cation-exchange mechanism. It has been found that within the ‘1212’
structure (between Tl-1212 and Hg-1212), the cation exchange process is
completely reversible and the direction of the process is determined by the
relative population ratio of Tl and Hg cations. The cation exchange is
bidirectional since Tl (or Hg) cations are only weakly attached to the “1212”
lattice (see Fig. 4.1). The lattice decomposition temperature for Tl-1212 (or Hg1212) may represent the binding energy of Tl (or Hg) cations to the “1212”
57
lattice. This result suggests that the cation exchange could be completely
reversible and the direction of the process is controlled by the population ratio of
the new cation and the one to be replaced. The final material after the cation
exchange may be an alloy of the precursor and the targeted material if a finite
ratio is selected.
Fig 4.1 Schematic description of the Tl–Hg cation exchange occurring on
the “1212” structure. The crystal lattice remains nearly unchanged while
the superconducting transition temperature is altered between 85 and 90
K for Tl-1212, and 120 and 125 K for Hg-1212.
The high Jc of Hg-1212 film made from Tl-2212 film has been obtained by
generating micro-channels to facilitate Tl-Hg cation exchange on “1212” lattice
using reversible cation-exchange. We have also investigated the conversion from
Hg-1212 to Tl-2212 at temperatures for which recrystallization of the Hg-1212
58
lattice is unlikely to happen. We have found that this conversion can be completed
under high Tl vapor pressure via two steps: Hg-1212 to Tl-1212 through Tl–Hg
cation exchange followed by Tl-1212 to Tl-2212 through Tl cation intercalation.
The experimental results are reported in this chapter.
4.1 Generating Micro-Channels to Facilitate Tl-Hg Cation Exchange on
“1212” Lattice
I. Introduction
During the Tl and Hg cation exchange process, one particular remaining
question is on diffusion pathways. It is unclear whether the diffusion occurs layerby-layer along the c-axis of the film, which is normal to the film, or through the
film along certain channels of growth defects such as voids and then followed by
the a-b plane diffusion. The answer for this question may not be unique when
different precursor matrices are employed. For Hg-1212 films, either Tl-1212
(y=1 and z=1) or Tl-2212 (y=2 and z=1) can be used as the precursor films. The
precursor Tl-2212 has two Tl-O planes that collapse into one Hg-O plane during
cation exchange, resulting in lattice shrinkage of ~14% along the c-axis. Many
voids form during cation exchange from Tl-2212 to Hg-1212, in contrast to the
nearly unchanged dense and smooth film morphology in the process from Tl-1212
to Hg-1212 since Tl-1212 and Hg-1212 have nearly the same crystalline structure.
Interestingly, the Hg-1212 films obtained from Tl-1212 always have broader
superconducting transition and lower Jc as compared to the ones from Tl-2212
59
precursor films. It was hence suspected that the voids actually serve as diffusion
channels through the film thickness and therefore enables dominance of a-b plane
cation diffusion as shown in Fig. 4.2(b). In the case of Tl-1212 to Hg-1212 cation
exchange, the diffusion of the Tl and Hg cations may have to follow a layer-bylayer pattern, as shown in Fig. 4.2(a), due to lack of vertical channels through the
film thickness. It is well known that the c-axis diffusion speed of oxygen is
several orders of magnitude lower than that along the a-b plane because of the
layered structure of HTS materials. If Hg and Tl cation diffusion is similarly
anisotropic for the same reason, the efficiency of Tl-Hg cation exchange is much
higher in the case of Tl-2212 to Hg-1212. Given the time frame for cation
exchange from Tl-2212 to Hg-1212 is on the order of 45-60 minutes, the
conversion from Tl-1212 to Hg-1212 may be only partially completed. The mixed
phase of Tl-1212 and Hg-1212 may be responsible for the observed broad
superconducting transition as well as the lower Jc values as we discussed earlier.
It is important to confirm the role of the micro-channels in the cation
exchange process. Motivated by this, we have developed a high-pressure
annealing process. Using this process, micro-channels can be generated in the
“1212” films. We have found that the Tl-Hg cation exchange process from Tl1212 to Hg-1212 or vice versa can be significantly expedited in the presence of
these micro-channels. Consequently, the Hg-1212 films obtained from Tl-1212
precursor contained the micro-channels show comparable superconducting
60
properties to that from Tl-2212. In the next section, we will discuss our
experimental results in details.
Fig 4.2 Diffusion channel of “1212” structure (a) the diffusion of the Tl
and Hg cations may have to follow a layer-by-layer pattern. (b) The
voids actually serve as diffusion channels through the film thickness and
therefore enable dominance of ab-plane cation diffusion.
61
II. Experiment and Discussion
1. Sample preparation
Two types of Tl-1212 precursor films were prepared with one containing
no micro-channels (set A) and the other, micro-channels. A big piece of Tl-1212
thin film was deposited on single crystal (100) LaAlO3 substrates at room
temperature using dc magnetron sputtering, and then annealed at 840 ºC for 1 hr
in flowing oxygen using crucible technique. At this stage, there were no micro
channels on both films. The Tl-1212 film prepared was then cut into two pieces in
the middle. One piece of film was kept in its primitive state, marked with
precursor Tl-1212A, the so-called set A. We then purposely processed another
piece of Tl-1212 film in order to introduce micro channels by following two-step
cation exchanges. In the first step, the sample was sealed in an evacuated quartz
tube together with two pellets. One of the pellets was an unreacted fine ground
and mixed HgBa2Ca2Cu3Ox, and the other, a Ba2Ca2Cu3Ox pellet. The first pellet
served as cations vapor source, and the second vapor absorber. The weight ratio
of the former to the latter was 3:1. They worked together to establish stable
pressure of the desired cations (atoms) that can be diffused into the lattice. The
whole assembly was kept in a furnace at 700 °C for 12 hr. In the second step, the
film was processed at Tl-rich environments of the evacuated quartz tube at 730 °C
for 2hr. Similarly, the Tl-rich environment was established by putting an
62
unreacted TlBa2Ca2Cu3Ox with a Ba2Ca2Cu3Ox pellet. Later on by SEM
micrograph, one will observe that micro channels had been introduced by this
film that came out these two step cation exchange processing. This film, which is
mainly in Tl-1212 state, will serve as second precursor, marked with Tl-1212B,
the so-called set B.
After all proceeding preparation of the two precursors, i.e., Tl-1212A and
Tl-1212B, they were put into the sealed evacuated quartz tube together at 700 °C
for 12 hr. The outcome films were marked by Hg-1212A and Hg-1212B
accordingly.
2. Crystalline Structure
The crystalline structure and phase purity of the films were analyzed using
x-ray diffraction (XRD). Fig. 4.3 illustrated the XRD θ-2θ spectra of the films
described in the previous section. All films were all c-axis oriented. Fig. 4.3 (a) is
corresponding to the regular precursor Tl-1212A film; (b) Tl-1212B film with
micro-channels; (c) Hg-1212A film made from Tl-1212 film (d) Hg-1212B film
made from Tl-1212B. Comparing Fig. 2 (a) through (d), one can see only “1212”
phase existed for all four films, judging from their nearly identical structure. This
outcome was indeed very encouraging in terms of layer structure, although it was
unclear about the completion of the Hg-Tl cations conversion in each status by
checking XRD data alone. The data of measured Tcs and scanning electron
63
microscopy (SEM) micrographs taken respectively will unveil more interesting
features during the transformation of the films.
Fig. 4.3 XRD θ-2θ spectra of the sample films (a) a regular Tl-1212A
film annealed in an Al2O3 crucible in Tl vapor at 840ºC for 1 hour; (b)
the Tl-1212B film with micro-channels ; (c) the Hg-1212A film made
from the Tl-1212A film; (d) the Hg-1212B film from Tl-1212B film;
All films except Tl-1212A made in a sealed quartz tube in Hg vapor at
700º C for 12 hours to get target Hg-1212 films or in Tl vapor at 730º C
for 2 hrs to achieve target Tl-1212B films.
3. Surface Morphology
Along the lines of the expectation based on the model established for
cation exchange processing technique, far better surface morphology was seen in
all the films generated from the cation exchange between Tl-1212 and Hg-1212,
compared with that of the films prepared from Tl-2212 precursors. The SEM
64
micrographs taken from all the four films were exhibited in Fig.4.4 (a) to 4.4(d),
respectively. The surface morphology of the precursor Tl-1212A shown in Fig.
4.4(a) is very smooth. After cation exchange at 700 °C for 12 hr, the surface
morphology of Hg-1212A inherited the excellent quality from its precursor [see
Fig. 4.4(c)]. Only a few small voids have been seen. It was no surprise to see this
outcome, according to the diffusion mechanism model established in our previous
work, simply because of no double- to single-layer transition involved. Precursor
Tl-1212B possessed also good surface morphology [Fig. 4.4(b)]. Interestingly,
some micro channels of submicrometer dimension had been introduced
successfully, in line with the expectations based on the diffusion model
established previously. After final cation exchange in the Hg-rich environment,
the sizes of micro channels on Hg-1212B film increased (Fig. 4.4(d)).
The
evolution of these vertical channels indeed evidenced the diffusion mechanism
governing the cation exchange process. The addition of these microchannels
could benefit high field applications by providing flux pinning. We will come
back to this point soon regarding the current density of the Hg-1212 films.
65
Fig. 4.4 scanning electron microscopy images of: (a) the regular Tl-1212A;
(b) The Tl-1212B film; (c) The Hg-1212A film made from Tl-1212A; (d)
The Hg-1212B film from Tl-1212B. (e) The Hg-1212AA film from Hg1212A film
4. Superconducting Properties
Fig. 4.5 depicted the temperature dependence of the magnetic
susceptibility of Hg-based and Tl-based films measured in a magnetic field (H)
applied along the normal of the film. In the precursor status (see the curve marked
with Tl-1212A in Fig. 4.5), the measured Tc value was 84 K. After first cation
exchange in Hg vapor surrounding, the outcome film should be Hg-1212 by
original design. The measured Tc value was 116 K, in the typical range of Hg1212 films. However, the transition edge was much broader than a typical one in
an HTS film, but no visible double shoulder shown in this case, which hints an
66
interesting mixture status of the film, i.e., an alloy phase of Hg-1212/Tl-1212 was
formed (refer to the curve marked with Hg-1212A in Fig. 4.5), consistent with the
theoretical prediction previously. For Tl-1212B, the surprisingly higher Tc value
implies another mixture of Tl-1212 with Hg-1212, but Hg concentration was not
high, judging from the transition edge. A typical Hg-1212 Tc-H curve was
achieved and the unwanted Tl-1212 phase was diminished to be negligible in Hg1212B film. This suggested the multiple-run trip between Tl-1212 and Hg-1212,
and consequent formation of the micro channels, was crucial for fabricating a
purer Hg-1212 film.
One may argue that solely extending the processing time of the first cation
exchange could work the same way. To answer this question, another experiment
had been conducted employing the identical setup and conditions with the sample
Hg-1212A, only helping us to conclude that the purity of the outcome Hg1212AA film did not show any improvement even the processing time doubled.
Actually, both Tc and Jc properties became even worse if purely doubled the
processing time. One can see this clearly from the curves marked with Hg1212AA in Fig. 4.5 and Fig. 4.6, i.e., no improvement see after doubling the
processing time in Hg-rich environment. By SEM micrograph, merely doubling
processing time in Hg vapor was unable to introduce micro channels.
67
2
Susceptibility (mA.cm )
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0
-3.5
-4.0
-4.5
-5.0
-5.5
Tl1212A
Hg1212A
Tl1212B
Hg1212B
Hg1212AA
0
20
40
60
80
Temperature (K)
100
120
Fig. 4.5 Magnetic susceptibility as a function of temperature measured in
zero-field-cool mode for the superconducting films. The applied field is
10 gauss and perpendicular to the film.
Then one may ask: what was major cause for this big difference? Let us
look back closely to all the processing parameter to answer this question. When
we converted Hg-1212 into its Tl-1212 target film, the temperature was set at 730
°C for 2 hr. At this temperature, the Hg cations as well as Tl ones can escape from
their equilibrium sites easier for the reason of higher stimulating energy. Owing to
the dominant Tl surrounding, the Hg cations tended to make their way out and
resulted in channels vertically, according to the diffusion mechanism of cation
exchange processing. Jcs were calculated using the Bean model from the
magnetization vs. magnetic field hysteresis loops measured at different
temperatures. The magnetic field was applied along the normals of the films. Fig.
4.6 showed comparative data of Jc as function of field at different temperatures
for the pair of representative Hg-1212A Hg-1212B films.
68
(a)
Jc/Jcself(5K)
1
7
2
Jc(A/cm )
10
0.1
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Field(T)
Hg-1212A
Hg-1212B
Hg-1212 from Tl-2212
Hg-1212AA
6
10
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Field(T)
1
Jc/Jcself(77K)
(b)
6
10
0.1
0.01
1E-3
2
Jc(A/cm )
5
10
1E-4
0.0 0.1
0.2 0.3
0.4 0.5 0.6
Field(T)
4
10
3
10
0.0
10
7
10
6
0.1
0.2
2
Jc(A/cm )
(c)
10
5
10
4
10
3
10
2
0.3 0.4
Field(T)
0.6
Jc/Jcself(100K)
1
0.1
0.01
1E-3
0
0.5
200
0
400 600
Field(Gauss)
200 400 600 800 1000
Field(Gauss)
800
1000
Fig 4.6 The Jcs of all Hg-1212 films at different temperatures (a) at 5K,
(b) at 77K and (c) 100K and the inlets are the normalized Jc
69
Three typical surrounding temperatures were set at 5 K, 77 K, and 100 K,
respectively. Two striking features were seen from the graphs. Firstly, remarkable
increase of Jc values obtained in Hg-1212B compared with that from Hg-1212A.
Based on the analyses early on, the film Hg-1212A consisted of a mixture of Hg1212 with Tl-1212. The ionic radius of Tl element was reported as 1.50 Å,
whereas ionic radius of Hg element was 1.02 Å. This might result in mismatch of
the lattice, consequently strains of the grain boundaries thus misorientation
between them. This could limit the current density of the film [18]. When the
phase of the film was purer, the strains lesser, thus higher the Jc value.
Another striking feature in all three cases was the superior Jc values for
higher magnetic field, especially in the film Hg-1212B. One can see this from the
crossover of the Jc curve at certain field values in 77 K and 100 K. In order to see
this clearer, we normalized Jc values for all the three cases and included them in
the insets. A great advantage of type-II superconductors is the large magnetic
fields. In our layered structure HTS film, the vertical channels (voids) of
micrometer dimension, though undesirable for the microwave related applications,
served here as parking spots to trap the fluxes in the film when the Lorenz force to
push them out of the film to reach diamagnetic state. These naturally developed
columnar defects in the multiple-run cation exchange processing remarkably
enhanced the current density in the high magnetic field, which other techniques
need a lot extra efforts to do the job.
70
Previously, Hg-1212B film suggested purer phase, thus sharper transition
edge and clean surface morphology seen. This deduction can be confirmed further
by R-T curves of the Hg-1212 films. In Fig. 4.7, the upper curve was
corresponding to Hg-1212A film, the lower one the Hg-1212B.
One can see although the Tc value in film Hg-1212B was little lower than
that of Hg-1212A, the much lower resistivity hinted high phase purity in the film
Hg-1212B. This was consistent with the explanation of the purer Hg-1212 phase
formation previously. In film Hg-1212A, the coexistence of Tl-1212 and Hg-1212
increased the discontinuity (inhomogeneity) possibly in unit cell scale, thus the
number of extra barriers the carriers need to jump across, like we mentioned
briefly in the section regarding Jc values before.
Fig. 4.7 Temperature dependence of resistivity (ρ) of Hg-1212A and Hg1212B films
71
III. Conclusion of This Section
To conclude, we have successfully conducted three-runs of reversible
cation exchange between epitaxial c-axis oriented Hg-1212 film and Tl-1212 film,
starting from Tl-1212 precursor film and elucidated the diffusion mechanism
governing the cation exchange processing. Furthermore, the vertical channels
developed during consecutive cation exchange processing functioned as flux
pinning centers, which are responsible to the obviously increasing of the Jc values
in higher magnetic field as well as the overlapping structure in the normalized Jc –
H curves of Hg-1212 films. Apparent formation of the alloy Hg-1212 with Tl1212 had been seen for two intermediate states during the three runs of cation
exchange processing. The remarkable increase of critical current density Jc of Hg1212 film from third cation exchange conversion hinted the better phase purity
achieved after three cation exchange conversions, which was supported by the
corresponding R-T curves from the same films. The reversible cation exchange
might be a good way to fabricated Type II High Tc superconductors, useful for the
high field applications, without extra efforts and hence extra cost.
4.2 Converting Hg-1212 to Tl-2212 via Tl–Hg Cation Exchange in
Combination with Tl Cation Intercalation
I Motivation
It is confirmed that the cation exchange is reversible between “1212”
lattice in last section. This result raises an interesting question of whether the
72
same or a similar mechanism applies to the cation exchange between Tl-2212 and
Hg-1212. An obvious complication in this case is the lattice variation along the c
axis. In the cation exchange from Tl-2212 to Hg-1212, two Tl–O planes in each
unit cell collapse into one Hg–O plane, leading to about 14% reduction in the caxis lattice constant from 1.48 to 1.27 nm. To convert the Hg-1212 back to Tl2212 via cation exchange the c-axis expansion is anticipated, which may be
prevented if the forward process from Tl-2212 to Hg-1212 involves a phase
transition. To pinpoint the cation exchange mechanism between Tl-2212 and Hg1212, we have investigated the conversion from Hg-1212 to Tl-2212 at
temperatures for which recrystallization of the Hg-1212 lattice is unlikely to
happen. We have found that this conversion can be completed under high Tl
vapor pressure via two steps: Hg-1212 to Tl-1212 through Tl–Hg cation exchange
followed by Tl-1212 to Tl-2212 through Tl cation intercalation. In this paper, we
report our experimental results.
II. Sample Preparation
The starting epitaxial Tl-2212 films were fabricated on LaAlO3 (LAO)
substrates using the crucible technique and the experimental details have been
reported previously [4.7]. Briefly, an amorphous Tl–Ba–Ca–O film with nominal
composition of 2.1:2:1:2 was deposited using dc sputtering and annealed at 820
◦C for 1.0 h in flowing oxygen in a closed crucible. The thickness of these Tl2212 films was around 300 nm. These samples were then subjected to single or
73
multiple cation exchanges in either Hg or Tl vapour. In each cation exchange step,
the sample was sealed in an evacuated quartz tube together with two pellets to
reach a controlled vapor pressure. One of the pellets was an unreacted
HgBa2Ca2Cu3Ox one for conversion from Tl-2212 to Hg-1212 (or an unreacted
TlBa2Ca2Cu3Ox one for conversion from Hg-1212 to Tl-2212) and the other, a
Ba2Ca2Cu3Ox pellet. The first pellet served as the Hg (or Tl) cation vapor source
and the second, a vapor absorber to stabilize the pressure during the processing.
The weight ratio of the former to the latter was 3:1 and the total pressure inside
the quartz tube was estimated at ~5–10 atm. The whole quartz-tube assembly was
kept in a furnace at 700 °C for 12 h for the conversion from Tl-2212 to Hg-1212.
For the reverse cation exchange from Hg-1212 to Tl-2212, processing in Tl vapor
at 760 °C for 2.0 h was employed. It should be mentioned that the crystal lattice
decomposing temperature Tth is 770–790°C for Hg-1212 films in 0.9 atm pure
oxygen. At high Hg vapor pressures of several atmospheres employed in this
experiment, much higher Tth is anticipated for the Hg-1212 lattice. This means
that lattice decomposition and recrystallization at 760 °C is unlikely to occur.
III. Results and Discussion
1. Crystalline Structure
Figure 4.8 shows the x-ray diffraction (XRD) θ–2θ spectra taken on a
representative sample at different processing stages in two complete cycles of
conversion between Tl-2212 and Hg-1212 structures with (a) the starting Tl-2212
74
film; (b) after its first cation exchange in Hg vapor at 700 °C for 12 h; (c) after a
half-time of the second cation exchange in Tl vapor at 760 °C for 1.0 h (marked
with Tl-Interphases); (d) after completion of the second cation exchange in Tl
vapor at 760 °C for a total period of 2.0 h; (e) after the third cation exchange in
Hg vapor at 700 °C for 12 h; and (f) after the fourth cation exchange in Tl vapor
at 760 °C for 2.0 h. The conversion from Tl-2212 to Hg-1212 is nearly complete
except for a small volume per cent of remaining Tl-2212 phase, which is 6% and
12%, respectively, from Fig. 4.8 (a) to (b) and from Fig. 4.8(d) to (e). In a similar
way, the reverse conversions from Hg-1212 to Tl-2212 [Fig. 4.8(b)–(d) and (e)–
(f)] are also nearly 100% with negligible trace of any remaining Hg-1212 phase.
This observation, together with our recent result on the reversibility of cation
exchange between Tl-1212 and Hg-1212 [4.10], suggests that the cation exchange
is a simple perturbation over the volatile cations on the existing lattice and the
process is bidirectional, with its direction determined by the population ratio
between the two cations involved.
75
Fig. 4.8 XRD θ–2θ spectra of the sample films: (a) the starting Tl-2212
film; (b) after its first cation exchange in Hg vapor at 700 °C for 12 h; (c)
after a half-time of the second cation exchange in Tl vapor at 760 °C for
1.0 h; (d) after completion of the second cation exchange in Tl vapor at
760 °C for 2.0 h; (e) after the third cation exchange in Hg vapor at 700
°C for 12 h; and (f) after the fourth cation exchange in Tl vapor at 760 °C
for 2 h. All films were made in sealed quartz tubes except the starting Tl2212 film.
The conversion between Tl-2212 and Hg-1212, however, differs from the
conversion within the ‘1212’ structure because of the c-axis lattice variation.
From Fig. 4.8, the c-axis lattice constant was 1.48 nm for Tl-2212 and 1.27 nm for
Hg-1212. To understand how the structural change occurred during the
conversion from Hg-1212 to Tl-2212, some samples were processed at shorter
time in Tl vapor before the conversion was completed. One distinctive
observation on these samples was the large volume portion of the ‘1212’ phase.
As shown in Fig. 4.8(c) for an Hg-1212 sample processed in Tl vapor at 760 °C
76
for 1.0 h, the remaining ‘1212’ phase was 63%. It should be noted that Hg-1212
films can be converted completely to Tl-1212 ones at this same processing
condition in Tl vapor of ~1 atm. This leads one to suspect, which was later
confirmed in the study of the electromagnetic properties (details in the following),
that this ‘1212’ phase is a Tl-1212 phase. This means that the conversion from
Hg-1212 to Tl-2212 involved two steps as shown in Fig. 4.9. First, Hg cations on
the ‘1212’ lattice was replaced by Tl ones, which can be completed in about 1.0 h
at 760 °C and in Tl vapor of ~1 atm and a much shorter period at higher Tl vapor
pressures. This Hg-1212 to Tl-1212 conversion was then followed by
intercalation of Tl cations into the ‘1212’ lattice for the ‘2212’ lattice to form. The
high Tl vapor pressures played a critical role in facilitating the intercalation. It
should be mentioned that a similar intercalation process has also been reported for
iodine in Bi-based HTS with similar layer structure [4.7-4.9].
Fig. 4.9 Schematic description of the two steps of the conversion from
Hg-1212 to Tl-2212.
77
2. Surface Morphology
The surface morphology of the samples after each consecutive processing
step was analyzed using scanning electron microscopy (SEM). Fig. 4.10 includes
the SEM micrographs taken on a Tl-2212 sample through two round trips of
conversions: (a) after the first cation exchange in Hg vapor; (b) after the second
cation exchange in Tl vapor; (c) after the third cation exchange in Hg vapor; and
(d) after the fourth cation exchange in Tl vapor, corresponding to the steps shown
in Fig 4.8(b), (d), (e) and (f), respectively.
Fig. 4.10 SEM images of a representative sample after several cation
exchanges: (a) after the first cation exchange in Hg vapor from a Tl-2212
precursor film; (b) after the second cation exchange in Tl vapor; (c) after
the third cation exchange in Hg vapor; and (d) after the fourth cation
exchange in Tl vapor.
78
Overall, the surface morphology experienced minimal changes after two
cycles of conversions between Tl-2212 and Hg-1212 except getting slightly
denser with each additional processing step. Besides many terrace-like surface
steps of increasing dimension with further processing, negligible impurity phases
were observable on the surface of the sample, suggesting that phase
decomposition during the processing was unlikely.
3. The Superconducting Properties
The superconducting properties of the sample were measured using a
Quantum Design SQUID magnetometer. The magnetic moment (M) as a function
of temperature (T) on the same sample shown in Fig. 4.10 after each
corresponding processing step is plotted in Fig. 4.11(a). The applied magnetic
field was 5.0 Oe along the normal of the film and the M–T curves were taken in
the zero-field-cooling mode. The two curves measured after the first (solid
squares) and third (open squares) cation exchange both in Hg vapor showed a
superconducting transition temperature Tc around 120 K, which is consistent with
the value expected for Hg-1212 film. This, on the other hand, excludes the
possibility of Tl-1212 being the dominant phase. The transition width of the M–T
curve for the latter is slightly broader possibly due to the higher remaining Tl2212 phase (12%) in the sample after this run [Fig. 4.8(e)] as compared to 6% Tl1212 remaining phase in the first run [Fig. 4.8(b)]. On the other hand, the two M–
T curves after the second (solid triangles) and fourth (open triangles) conversion
79
in Tl vapor nearly coincide with Tc = 105 K as expected for the Tl-2212 phase.
Also included in figure 4.11(a) is the M–T curve (solid circle) for the sample
shown in Fig. 4.8(c). The lower Tc = 100 K indicates the predominant Tl-1212
and Tl-2212 phases, instead of the Hg-1212 one in this sample. This confirms that
the conversion from Hg-1212 to Tl-2212 takes a two-step scheme with a cation
exchange from Hg-1212 to Tl-1212 followed by Tl cation intercalation in a Tl1212 lattice to form the Tl-2212. Fig. 4.11(b) compares critical current density Jc
as a function of magnetic field (applied along the normal of the film) at T = 5 and
77 K, respectively, for the same sample in Fig. 4.8(b) and (e). At 5 K, the Jc value
was nearly unchanged after a round trip of conversion from Hg-1212 to Tl-2212
and back to Hg-1212. At 77 K, the slightly reduced Jc in lower fields after this
round trip may be attributed to the slightly higher volume portion of the Tl-2212
remaining phase.
The reduction of pore (or voids) population may also contribution to the Jc
decrease in low magnetic fields since pores serve as strong pinning centers for
magnetic vortices. Nevertheless, the Jc values observed in this sample are in the
range for our high-quality Hg-1212 films. A similar trend was observed for the
same precursor Tl-2212 sample (stars) after the second (solid triangles, after one
cycle from the precursor Tl-2212 to Hg-1212 and back to Tl-2212 conversion)
and fourth (open triangles, after an additional cycle from Tl-2212 to Hg-1212 and
back to Tl-2212) conversion in Tl vapor.
80
Fig 4.11 (a) Magnetic susceptibility as a function of temperature
measured in zero-field-cooling mode for a sample experiencing several
cation exchanges. (b) Comparison of the Jc values of the same sample in
Hg-1212 phase after the first and third cation exchange from Tl-2212. (c)
Comparison of Jc values of the same sample in Tl-2212 phase before any
cation exchange (marked with Pre-Tl2212) and after the second and
fourth cation exchange from Hg-1212.
The result is shown in Fig. 4.11(c). At 5 K, the precursor Tl-2212 film has
the highest Jc value, which decreases slightly after the first cycle while it does not
change much after the second cycle. At 77 K, on the other hand, a minimal Jc
81
change was observed after the first cycle, while some noticeable reduction was
seen after the second cycle. Since Jc sensitively dictates the changes occurring to
the sample microstructure, these minor changes in Jc values suggest that some
defect structural variation may occur during the processing.
IV. Conclusion of This Section
In summary, we have demonstrated the conversion from Hg-1212 to Tl2212 structure can be achieved at relatively higher Tl vapor pressure and the
conversion consists of two steps: from Hg-1212 to Tl-1212 via Tl–Hg cation
exchange on the ‘1212’ lattice followed by Tl-1212 to Tl-2212 via Tl cation
intercalation. We have shown that the changes in the sample’s physical properties
are minimal after the sample underwent two full cycles of cation exchange
processes. This result, together with our recent demonstration of reversibility of
cation exchange within the ‘1212’, suggests that the cation exchange is a simple
perturbation over the volatile cations on the existing lattice and the process is
bidirectional with its direction determined by the population ratio between the
replacing cation and the one to be replaced.
82
Chapter 5
Third-Order Intermodulation in Two-Pole
X-Band HgBa2CaCu2O6+δ Microstrip Filters
HTS microwave filters hold a great promise for applications because of
the significantly lower surface resistance (Rs) as compared to that of their normal
metal counterparts [5.1, 5.2]. This has prompted intensive studies in recent years
on the improvement of HTS microwave device performance particularly in the
high power range. Among many different materials studied, such as YBa2Cu3O7
(YBCO), Tl2Ba2CaCu2O8 (Tl-2212) and HgBa2CaCu2O6+δ (Hg-1212) [5.3-5.6],
Hg-1212 is of special interest because of its high transition temperature (Tc) above
120 K. Since a higher Tc allows higher device operation temperatures, a lower
cost is projected considering higher efficiency of commercial cryogenic systems.
In our previous study, we have observed low microwave surface resistance (Rs)
and high power handling capability in Hg-1212 films and microstrip resonators up
to 110 K [5.7]. More recently, we have fabricated Hg-1212 two-pole X-band
microstrip filters using a cation exchange process[5.8] and observed a low
insertion loss of 0.70 dB at 110 K, which is better than that of YBCO and Cu at
77 K[5.6]. These results have demonstrated that Hg-1212 is a promising
alternative material for passive microwave applications at operation temperatures
83
above 77 K.
5.1 Nonlinearity in HTS Passive Microwave Devices
Nonlinear effects in HTS passive microwave devices are considered to be
the major cause that limits the power handling capability of the devices. Therefore,
understanding the nonlinearity is of great importance to the application of the
HTS microwave devices. The nonlinear effects appear in various different ways
including:
I. Nonlinear surface impedance [5.20]
The HTS nonlinearity is believed to originated either from the RF
magnetic field or from RF current dependence of surface impedance, Zs = Rs + jXs,
of HTS materials. In the low field region (Hrf < 10 Oe), the weak links is regarded
as governing role for nonlinearity in the HTS film [5.9], whereas in the
intermediate field (10 Oe to 50 Oe at 77K), the measured R data for YBCO can be
fitted well with the following expression:
Rs (H rf ) = a ( f , T ) + b( f , T ) H rf2 ,
(1)
Where f is the frequency, T the temperature, b (f, T) is proportional to f 2. The
expression of the surface resistance above is consistent with the postulation that
the RF field is breaking Cooper pairs. Interestingly, Rs increases faster than H2 in
the high field (50 Oe to 300 Oe), suggesting that the losses in the high power
region may be determined by hysterestic losses.
II. Generation of harmonics
84
Like any other nonlinear elements in an RF circuit, harmonics can be
generated from a HTS device, especially for high incoming microwave intensity.
Macroscopically, the nonlinear effect can be treated by a nonlinear resistance.
dI
I (V ) = I (0) + ( dV
)V = 0 δV +
1 d 2I
1 d 3I
( 2 )V = 0 δV 2 + ( 3 )V = 0 δV 3 + O (δV 4 )
2! dV
3! dV
(2)
Since I (-V) = -I (V), the lowest harmonic is the third order one. Consider a
sinusoidal signal:
δV = v sin ωt
(3)
Substituting (3) into (2), the third harmonic term is
−
1 d 3I
( 3 )V =0 v 3 sin 3ωt
24 dV
(4)
Take the logarithm of the amplitude:
y = log[
1 d 3I
1 d 3I
( 3 )V =0 v 3 ] = log[ ( 3 )V =0 + 3x ,
24 dV
24 dV
(5)
where x = log v . In the x-y plane, (5) gives a straight line with a slope that equals
to 3.
III. The third-order intermodulation (IM3) [5.9].
When two signals at frequencies f1 and f2 with the same amplitude are
applied to a device, such as filter, the initial phase can be expressed as:
δV = v(sin ω1t + sin ω 2 t )
(6)
Instituting (6) into (2), a signal with frequency 2f1 - f2 will be generated by
nonlinearity. The third-order intermodulation frequency ( 2ω1 − ω 2 ) term is
85
1 d 3I
− ( 3 )V =0 v 3 sin(2ω1 − ω 2 )t
8 dV
(7)
The amplitude of the third-order intermodulation frequency (IM3) signal increases
with the amplitudes of the two input signals.
Although they are all related to the nonlinear surface impedance [5.10],
their relative impacts on the performance of microwave devices may vary greatly
in each special case. For example, in passive rf filters, IM3 is perceived to be the
most serious problem to deal with due to the generation of spurious signals within
the passing band of the filter, which consequently deteriorates the device
performance. The origin of the nonlinearity has been a debate and various
mechanisms have been proposed. Two popular models proposed explain the
mechanism of the nonlinearity in passive microwave devices based on fielddriven[5.11] or current-driven.[5.12] In the former, the nonlinearity was attributed
to the penetration of magnetic vortices while in the latter, the exceeding limit of
the rf current density. Since inconsistency was observed in devices of different
magnetic field configuration[5.13], the field-driven mechanism may have strong
limitations in explaining the nonlinearity. The current-driven mechanism has also
been investigated in HTS devices and the difficulties associated to this study are
caused by multiple current limiting factors, intrinsic and extrinsic, including
grain-boundary Josephson junction behavior [5.14, 5.15], pair breaking[5.16,
5.17], and vortex depinning[5.12]. Although some of the extrinsic effects can be
86
minimized by improving the HTS materials, it remains an intensive research topic
to untangle the intrinsic current-limiting factors, which may behave differently at
different temperatures [5.12, 5.18].
The microwave nonlinearity has not been investigated so far in Hg-1212
devices, despite its importance to the device applications and also to the
understanding of the nonlinearity mechanism. Motivated by this, we have studied
the IM3 in two-pole Hg-1212 X-band microstrip filters. We have made
comparisons between the dc critical current density Jc and the rf current density
JIP3 derived from the third-order intercept at a reduced temperature scale for both
Hg-1212 and YBCO filters of the same configuration. Our results suggest that the
nonlinearity IM3 correlates intimately with the magnetic vortex depinning in HTS
materials, which is consistent with the current-driven model. In this paper, we
report our experimental results and theoretical analysis.
5.2 Fabrication and Characterization of Two-Pole Hg-1212 Filters
5.2.1 Fabrication and Transmission Properties of Hg-1212, YBCO and Tl2212 filters
Two-pole X-band Hg-1212 microstrip filters were prepared in a two-step
process: photolithographically patterning the Tl-2212 precursor films into twopole band-pass filters followed by Hg vapor-annealing of the resulting
superconducting filters using the cation exchange process [5.8]. The thickness of
the Hg-1212 filters is around 0.44 µm. For comparison, filters of the same
87
geometry and configuration were also fabricated on YBCO and Tl-2212 films of
0.5 µm thickness. Silver electrodes were laid on the feedlines of the filters via a
shadow mask using dc magnetron sputtering. For YBCO and Tl-2212 filters, the
Ag contacts were deposited before lithography while for Hg-1212 filters, after the
cation exchange. All filters were fabricated on 5 mm (width) × 10 mm (length) ×
0.5 mm (thickness) single crystal (001) LaAlO3 (LAO) substrates. Fig. 5.1 shows
the normalized magnetic susceptibility of the Hg-1212, Tl-2212 and YBCO films
(before lithography) as function of temperature measured by a Quantum Design
superconducting quantum interference device magnetometer in zero-field-cooled
mode in 10 Oe magnetic fields applied along the normal of the film. The Tc values
are 118 K for Hg-1212, 88 K for YBCO and 102K for Tl-2212. A plot of the dc
critical current density Jc against the temperature is shown in Fig. 5.2 for Hg-1212,
Tl-2212 and YBCO films, respectively. At 77 K, the Jc values are ~1.15 MA/cm2
for Hg-1212, ~0.47 MA/cm2 for Tl-2212 and ~1.16 MA/cm2 for YBCO. These
values fall into both the Tc and Jc range, respectively, for high-quality Hg-1212,
Tl-2212 and YBCO films of the thickness of 0.5 μm.
88
Normalizexd EMU (a.u)
0.0
Films of
Hg-1212 (Tc=118 K)
Tl-2212 (Tc=102 K)
-0.2
YBCO (Tc=88 K)
-0.4
-0.6
-0.8
-1.0
0
20
40
60
80
100
120
Temperature (K)
Fig. 5.1 Magnetic susceptibilities as a function of temperature of the Hg1212 and YBCO films measured in zero-field-cooled mode. The
magnetic field was 10 Oe applied along the normal of the film.
Fig. 5.3 plots the frequency dependence of the S21 transmission for all three
types of filters. The insertion losses measured at 77 K are 1.7 dB for YBCO filter,
2.2 dB for Tl-2212 filter. They are plotted against the Hg-1212 result of 110 K
where the insertion loss is approximately 0.6 dB. Overall, the Hg-1212 filter
provides better performance over both the Tl-2212 and YBCO filters at an
operating temperature 33 K higher.
89
Fig. 5.2 Temperature dependence of critical current density (Jc) for all three types
of films.
0
-5
S21 (dB)
-10
-15
-20
-25
Hg @ 110K
YBCO @ 77K
Tl-2212 @ 77K
-30
10.0
10.5
11.0
Ins. Loss
0.6 dB
1.7 dB
2.2 dB
11.5
Frequency (GHz)
3-dB BW
550 MHz
650 MHz
660 MHz
12.0
12.5
Fig. 5.3 Comparison of plots of S21 vs. frequency for three types of filters:
Hg-1212, Tl-2212 and YBCO.
90
5.2.2 Comparison of Third Order Intermodulation of Hg-1212 Filters with
YBCO and Tl-2212 Filters
The IM3 signals were measured at several different temperatures in the
range between 77 K and 110 K. The third-order intercept point (IP3), which is
defined as the input power at which extrapolations of the fundamental and the
IM3 curves intersect, was extracted from the measurement. In general, a higher
IP3 value corresponds to a weaker nonlinearity and hence greater power-handling
capability. Fig. 5.4(a) illustrates a schematic of the experimental set-up for
measurement of the fundamental and IM3 signals. Microwave signals were
generated using two sources: Agilent signal generators E8257D and E8251A. An
Agilent microwave network analyzer E8362B was utilized as a spectrum analyzer
with its receiver function. Two inputs with the same power at different
frequencies (f1=11.105 GHz) and f2=11.110 GHz) were chosen near the resonant
frequency. The inset of Fig. 5.4(a) shows the layout of the two-pole microstrip
filter and the details of the dimension have been described elsewhere [5.6, 5.19].
Fig. 5.4(b) exhibits the input versus the output power at different temperatures for
a representative Hg-1212 filter. The measured output powers for both
fundamental and IM3 signals were linearly proportional to the input power within
the measurement range up to 25 dBm (the upper limit of our instrument).
Extrapolating both the fundamental and the IM3 signals to higher input powers
reveals the intersection point of the two curves and allows determination of the
IP3 value. At 77 K, the IP3 value is around 58 ± 1 dBm and it decreases with
increasing temperature. At 90 K, the IP3 is about 55 ± 1 dBm and at 110 K, 38 ± 1
91
dBm. It should be noticed that the IP3 value obtained at 110 K represents the best
reported so far for superconducting microwave filters. The observed slopes of the
IM3 signals in Fig. 5.4(b) were 2.7 at 77 K, 3 at 90 K, and 3.4 at 110 K,
respectively, which differ slightly from the constant theoretical value of 3[5.20].
Interestingly, a weak temperature dependence of the slope has also been observed
on the YBCO filters and the slope decreases with increasing temperature, in
agreement with what reported by other groups [5.21, 5.22]. It has been noticed
that at 77 K, the Hg-1212 and YBCO filters have comparable slopes on the IM3
curve (2.8 at 77 K for YBCO). However, the values of the slopes in YBCO filter
were systematically lower than that in Hg-1212 filter at the same reduced
temperatures [see the inset of Fig. 5.4(b)]. Since higher slope of the IM3 curve
leads to lower interception point between the fundamental and the IM3 curve,
lower IP3 or power handling capability is then expected from Hg-1212 at a given
reduced temperature. This difference between Hg-1212 and YBCO may be
attributed to the different magnetic vortex pinning strength of these two materials,
as we will discuss in detail later in this paper. Fig. 5.5 compares the IP3 values of
the Hg-1212, Tl-2212 and YBCO filters as function of temperature. In the
temperature range of 77 K to 110 K, the Hg-1212 filter exhibited higher IP3 than
that of the Tl-2212 and YBCO filter and the difference between the IP3 values of
three types of filters increases with temperature. At 77 K, the IP3 for Hg-1212
filter is 58 dBm, 1 dBm higher than that of YBCO (57 dBm) and 4 dB higher than
that of Tl-1212(54 dB), respectively. At 110 K, the Hg-1212 filter has a similar
92
IP3 of 38 dBm to that of YBCO at 85 K and Tl-2212 around 90 K. The higher
IP3 values of Hg-1212 filters are more or less expected and are attributed to the
higher Tc of Hg-1212 and suggest that Hg-1212 is indeed an alternative for
passive microwave devices operating at higher temperatures.
Fig. 5.4 (a) Schematic diagram of the experimental set-up for measuring
IMD signals. Inset: Design layout for the two-pole half-wavelength filter
with width of 0.7 mm. (b) Input power versus the output power at
different temperatures for the Hg-1212 filter. Inset: the slop of the IM3
curves against reduced temperature.
93
Fig. 5.5 Plot of the IP3 values for Hg-1212, Tl-2212 and YBCO filters
Fig. 5.6 Plot of the IP3 values for Hg-1212, Tl-2212 and YBCO filters at
reduced temperature scale. Inset: Temperature dependence of the dc
critical current density (Jc) for the three types of films before patterning.
94
Also worth mentioning is the 0.44 µm thickness of the Hg-1212 filter
which is slightly smaller than that of YBCO (0.50 µm). It has been reported that
the transmission properties of the microwave filters improve as the thickness
increases up to a certain range (0.8 µm) [5.3]. This implies that the IP3 values of
the Hg-1212 filter could be higher if the IP3 value scales with film thickness.
Since the higher Tc of Hg-1212 is the main reason for the higher IP3
values observed in Hg-1212 filters, the IP3 curves were replotted on the reduced
temperature (T/Tc) scale to eliminate the Tc effect and to facilitate a direct
comparison between Hg-1212, Tl-2212 and YBCO filters. As shown in Fig. 5.6,
better power-handling performance can be obtained from the YBCO filters at a
given reduced temperature. To understand the mechanism underlying this
performance difference, a plot of the dc critical current density (Jc) against the
reduced temperature is included in the inset of Fig. 5.6 for Hg-1212, Tl-2212 and
YBCO films, respectively. Interestingly, the Jc vs. T/Tc curves for these three
different materials show qualitatively similar trends to their IP3 vs. T/Tc curves.
Since Jc is determined by the strength of the magnetic pinning in a specific
material, the difference in the Jc vs. T/Tc curves of YBCO, Tl-2212 and Hg-1212
films has been attributed to the different magnetic vortex pinning strength of these
three materials. Tl-2212 is extremely two-dimensional. The magnetic vortices
formed in Hg-1212 have geometry of “pancakes” that are weakly interacting
along the c-axis [5.23]. This is in contrast to the regular vortices formed in the
three-dimensional YBCO. The “pancakes” vortices can be depinned much more
95
easily than the regular ones, which results in weaker magnetic vortex pinning in
Hg-1212 and Tl-2212 as compared to YBCO.
In order to make a quantitative assessment of the correlation between the
dc and rf properties, the rf current density JIP3 was calculated from the measured
IP3 values. The rf current I IP 3 can be derived from the measurement of the PIP 3
according to[5.12].
I IP 3 =
2 PIP 3
ZL
,
(1)
Where Z L is the transmission line impedance. In a microstrip resonator, the rf
current density maximizes near the edge of the microstrip and the edge current in
the microstrip resonator can be written as: [5.24]
j ( 0 ) wt
2λ
J =
within roughly λ
2
t
,
(2)
of the edges. Where λ is the penetration depth, w is
the width and t, the thickness of the strip, and the value j (0) can be calculated by
[5.24]
I = ∫ jds ≈
π
2
j (0) wt .
(3)
In the same way, the rf current density JIP3 in two-pole microstrip filter
can be approximately expressed as:
J IP 3 =
j IP 3 (0) wt
=
2λ
2 PIP 3
1
×
ZL
πλ wt
96
(4)
Thus, near the edge, the ratio of the intermodulation current density JIP3 to JIP3 at
77 K is
⎡ P (T ) ⎤
J IP 3 (T )
= ⎢ IP 3
J IP 3 (77 K ) ⎣ PIP 3 (77 K ) ⎥⎦
1/ 2
∗
λ (77 K )
,
λ (T )
(5)
where, the λ (T ) is the magnetic penetration depth that depends on temperature
via:
T
Tc
λ (T ) = λ0 [1 − ( ) 4 ]−1 2 .
(6)
Fig 5.7 compares the normalized J IP 3 J IP 3 (77 K ) with J c J c (77 K )
against the reduced temperature for Hg-1212, Tl-2212 and YBCO filters. It is
clearly shown that the normalized JIP3 (triangles) and Jc (squares) curves follow a
similar trend on the reduced temperature scale for the three types of filters. It is
well known that the dc Jc in an HTS film is limited mainly by the depinning of the
magnetic vortices. The best Jc value achieved in YBCO, for example, is at least an
order of magnitude lower than the theoretical depairing Jc. This differs from the rf
case where the nonlinerity or JIP3 is determined by different mechanisms at
different temperatures. In the low temperature range much below Tc, the dominant
mechanism is d-wave intrinsic while at high temperatures near Tc, it has been
anticipated that magnetic vortex depinning plays the dominant role [5.18]. The
similar reduced temperature dependence observed in the normalized JIP3 to that of
Jc suggests that the magnetic vortex pinning mechanism indeed determines, or at
97
least plays the dominant role on, the nonlinearity JIP3 in Hg-1212, Tl-2212 and
YBCO at elevated temperatures near Tc.
Fig. 5.7 Normalized JIP3 /JIP3 (77 K) with Jc/Jc (77 K) against reduced
temperature for Hg-1212, Tl-2212 and YBCO patterned into the same
type of microstrip filters.
It should be mentioned that the correlation between Jrf and Jc has been
studied by others [5.4, 5.12] while no consensus has been achieved. On YBCO
coplanar resonators, Lahl and Wördenweber reported the same maximum rf
current density Jrf, max derived from the measured breakdown power Pmax and the
dc Jc over the whole temperature range below Tc. They argued that the
fundamental limiting mechanism in the absence of thermal and grain-boundary
effects is given by dc Jc, which disagrees with observation of intrinsic d-wave
nonlinearity in high-quality YBCO films at low temperatures not very close to Tc
98
[5.18]. It should be noticed that the dc Jc values shown in Ref. 12 are a factor 2-3
lower than that reported for typical high-quality YBCO films of comparable
thickness of ~ 300 nm[5.25]. In fact, the normalized JIP3 values obtained in this
work are consistently lower than the dc Jc. On Tl-2212 hairpin resonators,
Willemsen et al [5.4] compared the curves of intermodulation critical current
density JIMD (derived from the intermodulation power PIMD) [5.24] with Jc at the
lower input power (from 0 to -40 dBm). Large discrepancy between the JIMD and
Jc was observed. The authors argued that the JIMD and Jc describe different
physical regimes with JIMD describes the low-power microwave behavior while Jc
characterizes the high-power dc behavior. It should be realized that Tl-2212 is an
extremely two-dimensional HTS system in which magnetic vortices form
“pancakes” that are weakly interacting along the c-axis. This results in much
weak magnetic pinning in Tl-2212 as opposed to the strong pinning in threedimensional YBCO. Similar to Tl-2212, Hg-1212 is also known as a twodimensional HTS system. The surprising similarity in the curves of the
normalized dc Jc and rf JIP3 against reduced temperature in YBCO and Hg-1212
filters strongly supports the current-driven mechanism in HTS microwave filters
and the prediction given by Oates18 that flux pinning plays a major role in the
nonlinearity in high temperature region. Indeed, the weaker pinning Hg-1212
shows lower dc Jc and rf JIP3 than that of the stronger pinning YBCO as
demonstrated in this work.
99
5.3 Summary of this Chapter
In summary, microwave nonlinearity has been investigated in X-band Hg1212 two-pole filters and comparisons were made with Tl-2212 and YBCO filters
of the same configuration. The power handling capability of the filter was
characterized by monitoring the third-order intermodulation signals. Higher IP3
values were observed in Hg-1212 filters, as compared to that of YBCO and Tl2212 ones, in the temperature range at and above 77 K. At 77 K, the IP3 is 58
dBm for Hg-1212, which is higher than that of YBCO filter by ~1 dBm and Tl2212 filter by ~4 dB. The difference between the IP3 values for Hg-1212, Tl2212 and YBCO increases monotonically with increasing temperatures. At 85 K,
the IP3 value for Hg-1212 is about 54 dBm, which is ~18 dBm higher than that of
YBCO. At 110 K, a substantial IP3 of 38 dBm remains in Hg-1212 filter,
demonstrating that Hg-212 could be a promising alternative material for
microwave passive device applications at temperatures above 77 K. In addition,
the curves of the normalized dc critical current density Jc and the normalized rf
current density JIP3 against the reduced-temperature have a similar trend for Hg1212, Tl-2212 and YBCO, respectively, suggesting that flux pinning is
responsible for the microwave nonlinearity in HTS films at high temperatures.
100
Chapter 6
Conclusions and Outlook
I. Conclusions
In investigation of underlining mechanism and the improvement of the
cation exchange processing, there were three major achievements. Let me
summarize them one by one. We have fabricated epitaxial c-axis oriented
(Hg0.94Re0.06)Ba2CaCu2O6 films by replacing the Tl cations from an epitaxial
(Tl1.88Re0.12)Ba2CaCu2Ox precursor films in the cation-exchange process. It was
found that the presence of nonvolatile Re on the precursor lattice pins the lattice
locally so as to reduce the large-scale lattice collapse, which occurs on undoped
Tl-2212 precursor lattice and typically results in micrometer size voids in Hg1212 films after the cation exchange processing. By pinning the lattice with Re
doping, the void size has been reduced by an order of magnitude and the surface
morphology has been improved dramatically. In addition, this result has also
demonstrated for the first time that Tl-2212 precursor lattice doped with
nonvolatile elements on the volatile Tl sites can be employed for epitaxy of
chemically doped Hg-1212 films in cation exchange process, enabling tailoring
microstructure and physical properties of Hg-1212 films in a much controllable
fashion.
101
Reversibility in cation exchange has been proven by solid experimental
work and theoretical analyses. Between 1212 phase of Hg-based and Tl-based
HTS films, we have successfully conducted three-runs of reversible cation
exchange
between
epitaxial
c-axis
oriented
HgBa2CaCu2O6
film
and
TlBa2CaCu2Ox film, starting from TlBa2CaCu2Ox precursor film and elucidated
the diffusion mechanism governing the cation exchange processing. Furthermore,
the vertical channels developed during consecutive cation exchange processing
functioned as flux pinning centers, which are responsible to the obviously
increasing of the Jc values in higher magnetic field as well as the overlapping
structure in the normalized Jc –H curves of Hg-1212 films. Apparent formation of
the alloy Hg-1212 with Tl-1212 had been seen for two intermediate states during
the three runs of cation exchange processing. The remarkable increase of critical
current density Jc of Hg-1212 film from third cation exchange conversion hinted
the better phase purity achieved after three cation exchange conversions, which
was supported by the corresponding R-T curves from the same films. The
reversible cation exchange might be a good way to fabricated Type II High Tc
superconductors, useful for the high field applications, without extra efforts and
hence extra cost.
Between Tl-2212 and Hg-1212 phase of the films, we have demonstrated
the conversion from Hg-1212 to Tl-2212 structure can be achieved at relatively
higher Tl vapour pressure and the conversion consists of two steps: from Hg-1212
to Tl-1212 via Tl–Hg cation exchange on the ‘1212’ lattice followed by Tl-1212
102
to Tl-2212 via Tl cation intercalation. We have shown that the changes in the
sample’s physical properties are minimal after the sample underwent two full
cycles of cation exchange processes. This result, together with our recent
demonstration of reversibility of cation exchange within the ‘1212’, suggests that
the cation exchange is a simple perturbation over the volatile cations on the
existing lattice and the process is bidirectional with its direction determined by the
population ratio between the replacing cation and the one to be replaced.
Regarding characterization of the microwave devices, microwave
nonlinearity has been investigated in X-band Hg-1212 two-pole filters and
comparisons were made with YBCO filters of the same configuration. The power
handling capability of the filter was characterized by monitoring the third-order
intermodulation signals. Higher IP3 values were observed in Hg-1212 filters, as
compared to that of YBCO ones, in the temperature range at and above 77 K. At
77 K, the IP3 is 58 dBm for Hg-1212, which is higher than that of YBCO filter by
~1 dBm. The difference between the IP3 values for Hg-1212 YBCO increases
monotonically with increasing temperatures. At 85 K, the IP3 value for Hg-1212
is about 54 dBm, which is ~18 dBm higher than that of YBCO. At 110 K, a
substantial IP3 of 38 dBm remains in Hg-1212 filter, demonstrating that Hg-212
could be a promising alternative material for microwave passive device
applications at temperatures above 77 K. In addition, the curves of the normalized
dc critical current density Jc and the normalized rf current density JIP3 against the
reduced-temperature have a similar trend for Hg-1212 and YBCO, respectively,
103
suggesting that flux pinning is responsible for the microwave nonlinearity in HTS
films at high temperatures.
II. Outlook
Maintaining momentum accumulating from the substantial works
performed in the past pertinent to cation exchange processing and relevant
applications in our group, remarkable progress has been achieved through
research work activities in my thesis. These achievements kick doors widely open
towards fundamental science as well as applications. It is extensively accepted
that one of the important driving forces in HTS field is the applications of the
superconductors. With the maturity of the cation exchange methodology,
application push will be a fruitful direction to go along with Hg-based HTS.
The binding energy of Cooper pairs in a superconductor is of tens µeV to
tens of meV, depending on if surrounding temperature (external magnetic field) is
at proximity of Tc (Hc) or far away from the value. [6.1, 6.2] The absorption of a
single optical photon (energy of 1.2 eV at a wavelength of 1µm) can therefore
break a large number of Cooper pairs and hence create quasiparticles. The
corresponding changes of microwave properties can be used as a sensing means to
detect photon flux ranging from X-rays to THz wave at different temperature
[6.1-6.3]. In another end, the combination of the quasiparticles can generate
photons with THz frequency. In short, HTS cuprate superconducting materials
have drawn great attention in photonics sector due to their excellent transparency
and strong photoconductive effect and pyroelectric effect in near-IR through far104
IR waveband (THz) [6.1-6.6]. This intrinsic correlation between THz wave and
HTS material family has been envisioned as one of the great potentials of the HTS
applications.
Terahertz (THz) electromagnetic (EM) wave, which spans from 100 µm to
1000 µm in wavelength (or hν ≈1.24~12.4 meV in photon energy) has attracted a
lot of attentions in recent years due to its broad spectrum of potential applications.
[6.1] Among these applications are biological use in many sectors, such as
medicine (disease and wound states, skin hydration, plaque, and bone density)
homeland security (biological threat detection and explosive materials detection),
astronomy exploration (planetary science and life detection), biochemistry
(pharmaceutical, DNA analysis), food industry (on-line water content monitoring).
Emerging THz wave imaging has become a complement or substitute to X-rays or
MRI, particularly for organic substances because of its intrinsically non-ionizing
attributes.
In the massive research work related to this rapidly growing field within
last decade, tremendous efforts have been made on THz sources developments,
while much less efforts on detection side. Although THz imaging is highly
promising simply because of their intrinsic match of various fundamental
resonances of matters, such as phonons, molecule rotations, intraband electronic
transitions, etc, reports regarding detectors development are much less than
sources investigation for the rarely explored EM band. It is believed that
increasing the sensitivity of the detector would go a long way towards real
105
applications more efficiently in the standpoint of economics. Currently, most THz
detectors can only get intensity of total THz spectrum they see. It is highly
desirable to get a detector, which can achieve the entire spectrum of interest to
identify the target materials under investigation by comparing against the
signature database of THz frequency regime.
Commercial uses for THz sensors and sources are just sprouting as the
technology enables new instrumentation and measurement systems. However,
generation and detection of THz wave are still of the state of art, particularly,
effectively detecting of THz electromagnetic wave is still one of the major
roadblocks to the extensive applications of THz technology. The existing THz
detection technologies and their availability are as follows: [6.1]
LHe-cooled detectors
– Bolometers - commercially available, NEP~10-12 - 10-13 W/Hz 1/2
– Photoconductive Detectors – commercially available, NEP~10-15 W/Hz1/2
Room temperature mixers
– Schottky barrier diodes – ~commercially available, NEP~10-19 W/Hz1/2
LHe-cooled mixers
– SIS mixers – not commercially available, NEP~10-20 W/Hz1/2
– Hot-Electron-Bolometers – not commercially available, NEP~10-20
W/Hz1/2
There are advantages and disadvantages to all of them with much room for
improvement and further development.
106
Among cryogenic detectors, superconducting detectors are especially
attractive because thin-film deposition and lithographic patterning techniques may
be used to produce large arrays. Recently, a new detector concept based on the
microwave measurement of the complex impedance of a thin superconducting
film had been demonstrated with low temperature superconductor aluminum
deposited on sapphire substrate, allowing a simple frequency-domain approach to
multiplexing. [6.2, 6.3] This approach has been proven to have high sensitivity by
single X-ray photon detection with a high signal-to-noise ratio and a measurement
of the detector noise.
Seeing the broad application potentials of HTS materials and unique
properties of Hg-based HTS films, development of the photonics detectors and
sources will be one of my research interests in the near future.
Nonlinear resistance dependence is worthwhile to investigate with multipole filters, the same as the harmonic generation and intermodulation in these
filters. The research work along this line is great significance for applications of
the HTS films, as well as fundamental theoretical model, because the devices
based on nonlinearity can be derived from investigation activities.
The
underlining mechanism of the nonlinearity might provide clues about the
fundamental interaction that bind the Cooper pairs in HTS, and hence aid the
establishment of the theoretical model in HTSs, the counterpart of the BCS theory
HTS.
107
References
Chapter 1
[1.1]
M. Tinkham, Introduction to Superconductivity, Dover Publications, Inc.
New York, 2004.
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Publications
1. Hua Zhao, Jonathan R. Dizon, and Judy Z. Wu, “Third-order
intermodulation in two-pole X-band HgBa2CaCu2O6+δ microstrip filters”,
Appl. Phys. Lett. 91, 042506 (2007)
2. Hua Zhao, Jonathan R. Dizon, Rongtao Lu, Wei Qiu, and Judy Z. Wu,
“Fabrication
of
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hairpin
filter
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characterization of its third order intermodulation”, IEEE Transac. Appl.
Supercond. 17, 914-917 (2007)
3. Hua Zhao and Judy Z. Wu, “Converting Hg-1212 to Tl-2212 via Tl–Hg
cation exchange in combination with Tl cation intercalation”, Supercond.
Sci. Technol. 20, 327–330, (2007)
4. Zhongwen Xing, Hua Zhao, and Judy Z. Wu, “Reversible Exchange of Tl
and Hg Cations on the Superconducting “1212” Lattice”, Adv. Mater., 18,
2743–2746 (2006)
5. Jonathan R. Dizon, Hua Zhao, Javier Baca, Shramana Mishra, Rose Lyn
Emergo, Roberto S. Aga, Jr., and Judy Z. Wu, “Fabrication and
characterization of two-pole X-band HgBa2CaCu2O6+δ microstrip filters”
Appl. Phys. Lett. 88, 092507 (2006)
6. H. Zhao and J. Z. Wu, “Pinning lattice: Effect of rhenium doping on the
microstructural evolution from Tl-2212 to Hg-1212 films during cation
exchange”, J. Appl. Phys. 96, 2136-2139 (2004)
116
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